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- (2n+1)!/(2n+3)! simplified
- 🌟 Master the Magic of Calculus 🎓: From Domains to Limits, The Complete Guide to Understanding f(x) = √(x² – 1) 🚀
- 🌟 Unlock the Magic of Quadratic Functions! Master Difference Quotients with Easy Step-by-Step Guides for x², 2x + 4, and -3 + 2x² 🌟
- 🌟✨ Unleash the Power of PEMDAS: Become a Math Wizard! 🧙♂️🔮
- 📈 Unravel the Mysteries: Domains, Ranges & Graphs of tan(x) and tan⁻¹(x) 📚
- 🔍 “Cracking the Limit Code: Your Step-by-Step Adventure to Solve an Exhilarating Math Puzzle!” 🎉
- 🔍 Solving Money Mysteries: Unraveling Coin & Wage Puzzles 🧩💰
- 🔓 Unlock the Secrets 🤔: How the Function f(x) = (x² – 1) / (x² + 1) 👩🔬 Behaves as x ➡️ Approaches Infinity 🌌
- 🔓 Unlock the Secrets of Calculus: Master Continuity 🌟
- 🔥 Master the Intricacies of Chain Rule: Unveil the Derivative of |x| through √(x²) 📚
- 🧮 Discover the Equation: √(x²) = |x| 🚀
Cracking the Code of the Translated Circle: A Comprehensive Guide to the Domain and Range of (x – 2)² + (y + 1)² = 1
- 3 Vector Scalar Projection Calculator Step by Step Guide
- a – 2 [ -a – 3 ( -a – 4 ( -a + 1 ) + 2 ) + 3 ] + 4
- a paricle moves along a straight line and its position is given by s(t)=2t^3-18t^2+30t , where s is measured in feet and t in seconds.
- Algebraic Word Problems and Solutions
- Along what curve is ln(ln(x)+y) equal to 0 or where does it cross the xy plane?
- analysis of (x+2)/(x-2)
- analyze the graph of f prime of x raised to the the three over two
- analyzing functions of the rational type with roots, asymptotes, long division, first derivatives, second derivatives and graphing
- analyzing the derivatives of an absolute value function
- another form of a polar point
- AP Calculus FRQ Chart of Trends
- Applications of Function Inverses
- applications of rational functions
- arcsecant(x) function develop in great detail
- are the derivatives of ln of ax and ln of bx the same or different
- basic derivative facts
- basic stats with variances, populations, deviations, mean absolute deviation, sample standard deviation
- basics of compound interest
- basics of logarithmic functions
- basics of rational functions..domain..range, asymptotes..graphing..carefully explained
- basics-of-exponential-functions-graphing-asymptotes-domains-ranges-exponential-equations
- Calculate Savings per Person When Splitting the Bill with Friends
- Calculating the Limit of (1+x)^(1/x) as x → ∞
- calculus notes on integration with variable substitution
- Calculus question on maximizing or minimizing an integral
- Calculus reference sheet for students
- calculus-1-notes-11-21-2023-max-min-concavity-first-derivative-test-second-derivative-test-several-examples
- calculus-notes-on-finding-the-rest-times-and-total-distance-traveled-by-an-object-done-in-great-detail
- Can e^ln(x) represent x for x<0?
- complete-analysis-of-2x-squared-over-x-squared-minus-1-intercepts-first-derivative-concavity-domain-symmetry-vertical-asymptotes-horizontal-asymptotes
- complex expression with roots of negative numbers
- complex number interactive quiz questions
- Convergence and Summation Bounds of Series
- Cracking the Code of Linear Equations: From Fractions to Decimals and Beyond
- Deciphering the Nuances of Even-Powered Functions: A Detailed Analysis of x^2, x^4, (x-1)^2, and (x-1)^4
- degrees of freedom in an equation
- derivative of |x^2-1| using chain rule
- Derivative of |x^2-2|^2
- derivative of 2 raised to the absolute value of x.
- derivative of a function with nested square roots
- derivative of the absolute value of x minus 1
- derivative of the absolute value of x raised to the absolute value of x
- Derivative of x minus 1 raised to the square root of 2
- Derivative of x^4 using Pascal’s Triangle and the limit definition with careful explanations!
- Derivatives introduction: defining, finding with limit definition, tangent line equations and graphs!!
- derivatives of inverse trig functions
- derivatives of lnx and ln2x
- deriving derivative rules of tan inverse of x and sin inverse of x
- Detailed Examples of the Chain Rule
- determine if the set {0,1} is closed under addition
- Determining the Domain of ln(x² – 1)
- Determining the Range of x for a Linear Function Within a Given Tolerance
- difference between a function value and the average value of the function over 0 to 2
- differentials
- digging into perfect square trinomial factoring
- Discovering the Derivative of |x| for Negative Values: A Mathematical Exploration
- Disentangling local maxima, local minima, global maxima and global minima.
- does 1/2+1/4+1/16+.. converges or diverge?
- Does the following geometric converge or diverge?
- Does the integral of 1/(x^2+1) converge or diverge?
- Does the series e to the 1 over n divided by n cubed diverge or converge
- Does this function have both a global max and a global min?
- dolciani structure and method some solutions in great detail to questions in chapter 11
- domain and range of composite function
- domain of a function with nested square roots
- domain of ln of x over x minus 1
- domain of ln(|x|-2)
- domain of square root of 1 over x minus 1
- Domains and range of piecewise defined functions.
- examples of partial fractions
- exploration of a series
- Exploring and Understanding the Various Types of Discontinuities in Mathematical Functions
- Exploring the Limitless: The Domain of 1/(x-1)
- Exploring the Square Root of Absolute Value Functions
- exponential and log equations with applications
- expressions to be used in trig. substitutions
- factor an expression with fractional exponents
- facts about the inverse cosine function
- feasible regions
- find global max/min on quartic function x^4-98x^2+10
- Find the constant that makes a piecewise defined function continuous on negative to positive infinity. This one deals with a linear piece and a quadratic piece.
- find the differential for 5x^2+5x+3 and compare to the actual difference delta y
- Find the double sum of x+y when x goes from 1 to 5 and y goes from 1 to 4
- Find the error in the following calculation? Which step is not correct is the question. You’re finding the square root of negative seventy two.
- Find the interval of converges of a series
- find the principal value of ln of i raised to the i
- Find the range of y given by 1 divided by x minus 1
- Find the real part of 1/z, where z=a+bi
- find the real part of z cubed
- find the value of this expression with i and the roots of negative numbers
- Find the values of x for which the series converges.
- find x in the natural log of log base 2 of x plus 4 equals 8
- Finding an infinite limit with detailed calculations and a graph
- finding ranges
- Finding the domain of a function composition involving two fractions
- Finding the Range of x for f(x) = x^2 to be within 0.1 of 9
- Forming Set Complements Step by Step
- Functions: definition, sets, creating, evaluating, set-builder notation, interval notation, number lines
- future value, present value notes
- Graph Behavior of x³ – x² Near the Origin
- graphing a rational function with a vertical asymptote and a hole from repeating factors
- Graphing the Equation x² – y² = -4
- graphing-system-of-linear-inequalities-illustrated-in-great-depth
- hard limit..can you do it?
- how a single concept, the average, plays itself out in multiple ways
- How do we know that ∑ₙ₌₀^∞ rⁿ is the same as ∑ₙ₌₁^∞ rⁿ⁻¹?
- How to Crack the Euler Differential Equation: A Step-by-Step Guide You’ll Actually Understand!
- How to plot points, graph lines using intercepts, transform y-y1=m(x-x1) into y=mx+b with detailed examples
- implicit derivative notes with very detailed examples
- Implicit Differentiation Examples With Graphs
- Infinite limit with square root and rewriting with detailed explanations and a graph
- Integral of cos(x) from x=0 to x=2π
- integral of e^(kx) done step by step with great detail!! enjoy the thrilling fun of it and so much more
- Interactive Vector Addition Calculator: Master Vector Math Step-by-Step
- intro to l’hopital’s rule
- Introduction to Lines of Best Fit Using Matrices
- length of a complex number
- limit as n goes to infinity of e to the n over n factorial
- Limit of (x-1)/sqrt(x^2) as x goes to negative infinity
- limit of cosine of n over 3 to the n using hte squueze theorem
- limit of n to the one over n as n goes to infinity
- Limit of x^2 as x approaches 2 with the definition
- limit when x goes to negative infinity
- limits from graphs..detailed examples
- linearize (1+x)^(-3) at x=0 and find the interval so it’s accurate to within .1
- Linearize the sqrt of x at x=36 and graph
- local max or min for a curve defined over 0 less than x less than infinity
- log equations quizzes
- Logarithmic Differentiation Examples
- making a quadratic equation from irrational roots
- Master 2 Vector Subtraction with Step by Step Calculator
- Master the Magic of Math: Your Pathway to Factoring Like a Pro!
- Master the Mysteries of Polynomial Roots: Unveil the Hidden Power of Multiplicities with f(x) = x(x-1)²
- Master-3-Vector-Addition-With-Our-Step-By-Step-Calculator
- Mastering Linear Equations: From Matrix Magic to Movie Math
- Mastering Piecewise Function Graphs: A Comprehensive Guide
- Mastering Quadratic Equations: A Comprehensive Step-by-Step Guide
- Mastering Quadratic Equations: From Roots to Polynomials
- Mastering the Mystery of Square Roots and Inequalities: A Comprehensive Guide to Domain, Interval, and Set-Builder Notation
- math 111 notes 11 29 2023 applications of exponential models with several very detailed examples
- math 115 notes basics of using counting principle with cards and worms and combinations to find probabilities
- math quizzes
- math-111-notes-properties-of-logs-power-rule-difference-rule-product-rule-change-of-base-formula
- Matrix combinations using scalars, additions, subtractions and multiplications
- Matrix definition, example of making, adding, subtracting, reading entries from and reading dimensions of, equality of
- maximizing profit with linear programming …several very detailed examples with graphs
- mean value theorm applied to an exponential function
- mean, median, mode, range, deviations with several very detailed examples
- midpoint rule example with calculation and graph
- modulus behavior of 1 over z
- modulus of double z
- Notes on matrix applications
- notes with examples on annuities
- notes-doubling-time-tripling-time-quadrupling-time-for-investments
- PEMDAS exercise at a more advanced level that feels like an internet meme
- points in polar coordinates quiz question
- Polynomial Quiz
- present value of annunity notes in detail with multiple examples
- quadratic functions notes with graphs and solved problems
- quiz on factorizing sums of cubes
- Quiz on find the limit of e raised to the 1 over x
- range of a function with nested square roots
- Range of y equals e to the x by an algebraic process
- rationalize 0.072999…
- recognizing and factoring perfect square trinomials
- reducing a fractional expression that has fractions in exponents
- relating the remainder of a series to an integral using a picture
- relative growth rates for exponential growth
- rewriting absolute value functions using pieces
- sample quizzes
- Shifting Summation Indexes
- simple interest ideas with applications
- simplify (2n-1)!/(2n+1)!
- simplify i raised to the seventy third
- simplify i raised to the square of i
- Simplify i²³ / (i¹⁵ – i¹⁷) Explanation
- simplify the square root of the cube of i
- simplifying a complex expression with multiple roots of negative values
- solution to 2+ln|x|=5
- solve (x-1)^3-(x+2)^3=-(x-3)^2
- Solve sin(x)=0, cos(x)=0, tan(x)=0. These are elementary trig. equations.
- Solve the inequality 1/x<1/(x-1) step by step with a number line.
- Solving a hard exponential equation
- solving a rational inequality
- Solving an Inequality: 1/x < 1/(x-1)
- Solving cos(x)=sin(x) and cos(x)=-sin(x) in detail step by step
- solving linear and non linear systems with examples
- solving quadratic equations guided quizzes
- solving quadratic equations with steps quizzes
- Solving simple differential equations
- Solving the Second-Order Linear Differential Equations
- some solutions to dolciainis structure and method from pages 563 and 566
- sum of .1+.01+.001+.0001+…
- synthetic division quizzer with steps
- Take the Fun Piecewise Function Quiz – Test Your Math Skills Now!
- tangent line and secant line slopes using the mean value theorem
- The derivative of the function f(x) = sin(cos(3x)) with respect to x
- The Schrödinger Time-Independent Equation: Unveiling Quantum Mysteries
- the set of all ordered pairs
- to ride on the world’s fastest rollercoaster you must be at least 55 inches tall but less than 91 inches tall….
- transition math to calculus
- Trigonometric Equations: Solving for sin(x) = 1, cos(x) = 1, and tan(x) = 1
- Two cars are moving towards an intersection. One car is 150 meters north of the intersection and the other is..
- Ultimate guide to sqrt(x), sqrt(x+1), sqrt(x-1) with graphs and detailed information
- Understanding Differentiability: A Comparative Study of f(x) = x² and f(x) = |x| at x = 0
- Understanding how to approximate derivatives with the slope formula by using very tiny values of h
- Understanding Image Gradients
- Understanding Linearly Independent Functions or Sets
- Understanding Local Maximums in a Vast Landscape
- Understanding second partial derivatives with graphs
- Understanding Set-Builder Notation
- understanding the concept of a hole in a rational function graph. detailed steps and a graph.
- Understanding the inverse secant function.
- Understanding the Limit of |x|/x as x Approaches 0: A Comprehensive Guide
- Understanding the Square Root of the Absolute Value of a Complex Number
- unit circle with negative angles
- Unlock applications of linear systems through three detailed examples
- Unlock the concepts behind complex numbers
- Unlock the concepts behinds graphs that may or may not be functions!
- Unlock the domain of log(-5x+11) (base 4) with a graph and detailed discussions in inequality form, interval form and set-builder form
- Unlock the Enigma: Decode the Domain and Range of f(x) = -√(1 – x²)
- Unlock the key to x=-2x-(2x-1/3x+1) (linear equation)
- Unlock the keys to solving a variety of equations with factoring, square roots and grouping
- Unlock the limit of f(x)=2x+1 as x approach 2 by the defintion with epsilon and delta.!
- Unlock the limit of sin(2x)/(3x) as x goes to 0, step by step
- Unlock the Mathematical Universe: Exploring the Domains of 1/(3x + 2), √(3x + 2), and log(3x + 2)
- Unlock the Mysteries of e^x: A Journey Into Mathematical Excellence!
- Unlock the Mysteries of the Transformative Graph: 1/(x+1) + 2
- Unlock the mystery of domains of square root functions
- Unlock the mystery of intervals in algebra
- Unlock the mystery of limits at infinity with several different approaches for better understanding!
- Unlock the mystery of solving systems of equations using Gaussian Elimination
- Unlock the mystery of the neutron!
- Unlock the mystery of the non-existence limit
- Unlock the mystery of the proton!
- Unlock the Mystery of the Regular Singular Points in Differential Equations
- Unlock the Mystery: Why the Limit of |x+1|/(x+1) is Elusive
- Unlock the Paradox: Why the Limit of |x-1|/(x-1) Vanishes
- Unlock the power of visualizing the Graph of 1/(x+1)
- Unlock the Secrets of Calculus: Mastering the Limit of √(10 + 9x²) / (10 + 2x) as x → ∞ 🧠🔓
- Unlock the Secrets of Differentiation: Dive into the Power Rule with f(x) = 2 + 8/x + 6/x^2
- Unlock the secrets of double integrals!
- Unlock the Secrets of Linear Equations
- Unlock the Secrets of Odd-Powered Functions: A Comprehensive Guide to Understanding x¹, x³, and x⁵
- Unlock the Secrets of Root Multiplicity: A Deep Dive into the Behavior of f(x) = x(x-1)³ Near Critical Points
- Unlock the Secrets: Finding the Domain and Range of f(x) = √(1 – x²)
- Unlock your brain: find the domain of 1/(-5x+11)
- Unlock-3D-Vector-Subtraction-with-Our-Interactive-Calculator
- Unlocking the domain of a piece-wise defined function from a graph.
- Unlocking the Infinite Possibilities: The Domain of 1/x
- Unlocking the Mysteries of the Perfect Circle: Exploring the Domain and Range of x² + y² = 1
- Unlocking the mystery of 1/(x+2)+2, the graph and analysis of function!
- Unlocking the Mystery of the Limit of |2x + 1| / (2x + 1) as x Nears -1/2: A Revealing Mathematical Journey
- Unlocking the Secrets of Calculus: Approximating Derivatives with Average Rate of Change
- Unlocking the Secrets of Coefficients: A Journey from Simple Linear Expressions to Complex Polynomials
- Unlocking the Secrets of f(x) = x²(x-1): A Comprehensive Visual Guide
- Unlocking the Secrets of Linear Inequalities: A Comprehensive Guide to Understanding, Creating, Solving, and Mastering!
- Unlocking the Secrets of Right Triangle Trigonometry: From Basics to Real-World Applications
- Unlocking the Secrets of the Limit: A Joyful Dive into (3x + 1) / (x + 4) as x Approaches 5!
- Unveil the Secrets of the Enigmatic Graph: 1/(x-1) – 2
- Unveiling the Secrets of the Shifted Circle: A Deep Dive into the Domain and Range of (x – 1)² + y² = 1
- Using the Squeeze Theorem
- value of 1 divided by the square root of i
- various math quiz questions
- various more advanced factorization problems
- vertex of an absolute value function
- Very detailed explanations of solving 3 by 3 system using elimination and back-substitution
- volume in 3d space
- We are given that the sum of three numbers is 120. The second number is eight less than the first, and the third number is 1 1/2 times the second.
- What are two possible values of a and b so that a x² + b x + 5 has the value 1 at x=1.
- what happens if we show a curve crossing a vertical asymptote
- What happens to the graph of f'(x) at x=0?
- What happens to the horizontal asymptote of e to the x when we mirror across y equals x
- what happens to the range of a piece-wise defined function when we mirror across the x axis
- What is d/dx (∫ (d/dx x² dx))?
- what is e raised to the log base 2 of 5
- what is i raised to i where is the imaginary unit
- What is the derivative of 2x quantity cubed?
- what is the derivative of sinx raised to the cosine of 1 over x
- What is the derivative of x raised to the cosine of x
- what is the domain of this function?
- What is the Planck’s Constant
- what is the range of the function y equals 1 over x plus 1
- What is the sign of the natural log of a function given the function graph
- What is the square of the modulus of a complex number
- what is the square root of the negative x raised to the negative 2 equal to
- What should a be so that a⋅x² + 2x + 4 has the value 5 at x=1?
- what x in ln of ax equals b where for simplicity a and b are both greater than 0
- What’s 1/[log_2e(x)]
- What’s an electron, really!
- What’s ln of the log of base 2 of x plus 4 equal to 8
- What’s the domain of 1/ln(x)?
- What’s the slope of ln(ln(x)-y) at x=1 where ln(ln(x)-y) is 0.
- when are x and e raised to the ln of x equivalent
- Where does the series converge?
- where is f prime of x undefined given the graph of f below
- where is the mistake in the following calculation?
- which graph is the derivative of negative 3 times x squared
- Which is the graph of x squared over x squared minus 2
- Which step has the erorr to find the limit of (1+2x)^(1/x) as x goes to infinity?
- Work rate problem with two people where one takes 2 hours less to complete a job
- x and y intercept of a quadratic function with steps
- x^4-3x^2=0
- Home
- Unlock: step by step directions for finding the derivative of e^(2x)
- Step by step directions for finding the limit of csc x as x goes to π and tan(π/2) too!
- Partial Derivative Calculator
- integral of e the square root of x (integral e^sqrt(x))
- Step by step directions for finding the derivative of ln(cos(x))
- Solving 2cos^2(x)+sin(x)-1=0 step by step
- distributive property with only linear terms and multiple fractions in an equation
- Step by step directions for finding the integral of e^x cos(x)
- Step by step directions for finding the antiderivative of the square root of x
- age problem algebra
- Step by step directions for finding the derivative of the square root of x
- graphing lines by intercepts
- Step by step directions for finding the derivative of sin^2(x)
- Step by step directions for finding the antiderivative of e^sqrt(x)/sqrt(x)
- sigma notation basics with video
- Distributive Property: Simplifying Expressions with whole numbers, decimals, fractions
- Graphing a Line By X and Y Intercepts Workbook
- Example of a Trig Derivative (several examples)
- Step by step directions for finding the antiderivative of 1/sqrt(x) with graph and video
- limit of function with a hole
- simplifying complex mathematical expressions using the distributive property
- Finding Partial Derivatives of Exponential Functions with Negative Exponents, e^(-xyz)
- Adding Two Dimensional Vectors with Fractional Components
- The Integration of the Exponential Function e^(-x)
- Limit of the Cosine Function cos(1/x) as x Approaches Infinity
- solving the quadratic equation x² + 1 = 0
- forming a linear combination of two 2D vectors
- Step by step directions for finding the limit of (e^x-1-x)/x^2 as x goes to 0
- Step by step directions for finding the limit of (1-cos(x))/x^2 as x goes to 0 using L’Hopital
- graphical vector subtraction
- Learn how to find the limit of (1-cos(x))/x² as x approaches 0 without L’Hôpital’s Rule. The result is ½ using standard trigonometric methods.
- Find the limit of ln(x)/x as x approaches infinity.
- vector subtraction 3D vectors with integer entries
- subtracting 2d vectors with fraction entries
- limit from right and left with picture
- solving linear equations
- Guide to Graphing a 3D Vector: Easy Steps
- Booklet containing many examples of applying the chain rule in calculus.
- Finding limits of sequences booklet.
- extensive collection of graph paper
- Solving Linear Equations: linear equation with one fraction on the left side
- Converting a CDF to a PDF and finding a probability
- analysis of the trigonometric cosine function
- linear equation with two terms on the left side, one is a fraction
- Finding the antiderivative of ln(x)/x
- Locating points on a number line using division.
- Finding the area of a circle, step by step, with rounding to the hundredths place.
- Finding Eigenvalues of the given matrix
- Subtracting a Mixed Number from a Whole Number
- finding the tension and acceleration in a two block system
- algebraic vector subtraction two dimensional vectors
- Finding the antiderivative of sin(x)cos(x)
- Solving linear equations booklet.
- limit x^x
- vector grapher
- finding the derivative of e^(-x)
- finding the integral of e to the 2x
- limit x ^ (1/x)
- Unlock the Improper Integral of 1/x^2 from 1 to infinity
- converting r=3cos(theta) to rectangular form
- finding the integral of sqrt(1-4x^2)
- Finding a unit vector for a vector in three dimensions
- finding the antiderivative of sin^3(x)
- gradient calculator with multiple pieces of information
- Unlock the Secrets of Trinomials: Step-by-Step Guide to Mastering k(x) = -4x³ + 2x² – 6, h(x) = 3x³ – 5x² + 7, and More!
- Unlock the Secrets of Calculus: A Thrilling Step-by-Step Guide to Mastering the Antiderivative of 1/x²
- Unleash the Power of Integration: A Captivating Guide to the Antiderivative of 1/(1 + x²)
- finding the integral of ln(x)
- Discover the Magic of Calculus: A Comprehensive Guide to ∫ 1/(1 – x²) dx
- Unlock the limit ln(x)^(1/x) as x approaches positive infinity
- limit x^1/(1-x)
- Unlock the Secrets of Calculus: A Step-by-Step Guide to ∫ x sin(x²) dx
- Finding a unit vector in two dimensions between two points step by step for easy understanding
- finding the limit of xlnx as x goes to 0 from right
- Embark on a Mathematical Exploration: Unraveling the Gradient of f(x,y) = x² + xy + y²
- limit x^(x^2)
- limit cos(x)^(1/x)
- limit (1+P/x)^x
- Vector Addition: Combining Forces and Directions
- distributive property with only linear terms and multiple fractions
- Master the Equation: Definitive Graph for Solving 2sin²(x) – sin(x) – 1 with Precision in π/6 Units
- Exploring the Derivative of 1/x: A Calculus Adventure
- limit sin(x)^sin(x) as x approaches 0 from right side
- limit (1+1/x)^x
- sum of ages problem
- An Odyssey into 3D Space: Sketching the Enigmatic Plane f(x,y) = 4 – 2x – y
- forming linear combinations of vectors with three components
- simplifying a product of two exponential expressions with three different variables
- Unlocking the World of Algebra: Two Linear Equations
- simplifying a ratio of two exponential expressions
- limit x^[1/(x-1)] as x approaches 1 from the right side
- to simplify the expression (5w⁶)(6w¹⁰)(7w²), you can follow these steps
- graphing templates
- example of inequality with variables on both sides
- Explore the Elegance of Calculus: Unraveling the Derivative of 1/x⁴
- solve the linear equation 2x+4=6x-5
- linear equation with distributive property
- cups of sugar or cookies proportion
- equation with the distributive property on the right side
- linear equation with distributive property on one side
- Step by step, deciding whether a set is a function.
- 240 is 30% of what number?
- Step by step, what number is 75% of 90?
- mathematical set exercises
- Forming the cartesian product of two sets
- finding a missing value in a proportion
- distance proportion problem
- years until ages are equal age problem
- age problem involving number of years ago ages were equal
- unit circle pdf
- Master the Unmasterable: Your Ultimate Guide to Conquering Improper Integrals!
- master drawing vectors with our step by step guide
- Graphing Lines By X and Y Intercepts Workbook
- complex numbers booklet
- Master the Intricacies of Partial Derivatives: Unveil the Hidden Layers of Calculus and Unlock Your Full Potential
- Improper Integral 1/sqrt(x) from 0 to 4
- Unlocking the improper Integral 1/(x-2) from 1 to 3
- Improper integral e^(2x)/(1+e^(4x))
- Improper Integral e^-|x|
- Improper Integral 1/xln(x) From 3 To Infinity
- Improper Integral Rational Function 2 to Infinity
- Unlock the improper Integral 1/(3x+1)^2 From 0 To Infinity
- Improper Integral 1/(2x+1) From 0 to Infinity
- Improper Integral 1/ x from 1 to infinity
- Improper integral e^(3x) from negative infinity to 0.
- Improper integral of 2e^(-2x) from 0 to positive infinity
- Improper integral 1/(1+x^2) from 0 to infinity.
- integral 1/(1+x^2) from negative to positive infinity
- Improper integral 1/x^4 from negative infinity to negative one
- Improper integral 1/sqrt(x) from 4 to infinity
- Limit sin(2x)/x as x goes to 0, step by step
- Unlock the Secrets of Polynomial Factoring: Master Powerful Techniques to Simplify Complex Expressions!
- derivative of ln(sqrt(x))
- circuit with battery, switch and lightbulb
- Switches in series with circuit diagram and truth table
- Switches in parallel with diagram and truth tables
- Three parallel switch circuit diagrams with truth table
- inverter or not gate with diagram and truth table
- and gate with diagram and truth table
- Or Gate With Diagrams And Truth Table
- XOR Gate With Diagrams And Truth Table
- Dividing complex numbers a+bi over ci
- -2^3, -3^2,-4^3 (Examples of finding exponential expressions with negative bases and positive, whole number exponents)
- (-2)^3,(-2)^2,(-3)^2 (Examples of finding exponential expression values)
- (-1/2)^4 (Exponentiating fractional bases to positive, whole number exponents)
- two switches with NOT and AND gates circuit diagram
- Unlock the Power of NAND Gates: Your Ultimate Guide to the Universal Logic Builder 🌟🔐
- Showing a relation is not a function.
- Integral of x^4 between 0 and 1
- Unlocking solving literal equations!
- Unlock the secretes to linear equations with fractions and the distributive property
- Unlock the Secrets of Algebra: Master This Equation in Simple Steps!
- Linear Equation With Distributive Property On The Right Side With A Constant
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- Unlock: rationalizing fraction with a difference of two square roots in denominator
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- Step by step antiderivative of e^(2x)/(1+e^2x)
- Definite integral of x^2/(1+y^2) using a double integral from 0 to 1 for x and 0 to 1 for y.
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- Rewiting numbers as powers of ten
- Decimal to binary conversion form
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- Long example converting decimal to binary form
- adding binary numbers
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- Jared is 5 years older than Alma. In 9 years the sum of their ages will be 67. How old is Jared now?
- Find three consecutive odd numbers whose sum is 1359.
- Derivative of e^(x^2+4x+5)
- Implicit derivative example in step by step detail
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- Multiplying binary numbers
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- find the slope of a line that has a negative slope
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- derivative of sin(2x)
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- limit sin(6x)/2x with video
- Solving F=ma for a or m with video
- integral of 1/(sqrt(x)+x)
- factoring 1/[sqrt(x)+x]
- integral sqrt(x-1)
- simplifying a ratio of two exponential expressions
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- simplifying a ratio of two exponential expression with two uses of the distributive property
- exponential expression using distributive property with negative exponents
- simplifying a exponential expression with a fraction and the distributive property
- effective annual yield
- testing for x axis, y axis and origin symmetry with video
- graphing a parabola using a sequence of transformations
- parabola transformation with a vertical flip
- convert rcos(theta) to rectangular form with video
- why do the angles of a triangle add up to 180 degrees?
- vertex from parabola standard form
- Wave on a string simulation
- finding the domains and ranges for two different rockets
- total amount of money using interest at 5% after three months
- difference quotient for linear function
- difference between holes and vertical asymptotes with video
- equation of parabola found from three points with video
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- Solving proportions examples
- Sample of finding the average rate of change of a parabola
- Finding the average rate of change of a parabola with a negative slope
- Several examples of multiplying binomials using foil
- Factoring negative -1 from an expression
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- factoring by grouping example and factoring the gcf examples
- Factoring Trinomials Using the AC Method And Grouping
- types of intervals used in math with interval notation and number line
- Horizontal Shifts of functions
- transforming |x| into -2|x – 1| (absolute value transformation)
- LImit of x ln x as x approaches 0 from the right
- Factoring -4x^2+2x+30
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- converting feet cubed to inches cubed
- solving a quadratic equation with two terms
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- discriminant
- Quadratic-equation-complex-solution-no-perfect-square: -2x^2=3(x+2)
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- finding inverses of linear functions
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- How many laptops the math department can buy if they have 6500 to spend, have already purchased 30 textbooks that cost 116 each, and each laptop costs 439.
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- Which relation does not represent a function?
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- Unlocking the Secrets of Algebra: A Step-by-Step Guide to Solving a Quadratic Expression!
- A table of values showing the value of a laptop over the years. The value of the laptop decreases by 20% each year. The function that can be used to determine the value of the laptop for x years after the purchase is f(x) = 1250(0.8)^x.
- The number 5 in the function h(x) = -4.9x² + 6x + 5 represents the initial height of the ball. This is the height of the ball when it is released.
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- Detailed example of using the mean value theorem in calculus
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- Finding the max error for the sin(x) using its Taylor series
- find volume with disk method around y axis
- three examples of implicit derivatives
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- converting complex numbers from polar to cartesian form
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- several examples of finding the radius of convergence and interval of convergence of a power series
- proof of cauchy’s integral formual for f(a)
- motivation for the identity theorem in complex analysis using pictures
- seven important corollaries related to the identity theorem in complex analysis
- proving f(z) can be represented as a polynomial of degree <=n in complex analysis
- complex analysis series for cos(z)/z , pole of order 1
- complex analysis series for sin(z)/z
- complex analysis series for e^(1/z)
- finding on integral with Cauchy’s Residue Theorem in complex analysis
- Success Page
- Simulations
- derive the formula for the distance between a point and a plane in 3D space
- where are the graphs of x^2 and x^3 concave up/down?
- examples of inequalities in 3D
- example of limits in multivariable calculus one exists and one doesn’t exist
- concepts behind vector-valued function derivatives and an example
- detailed examples of solving radical equations ,including using graphs
- solving rational equations examples with graphs
- identify the curve defined by a vector-valued function
- Completing an ANOVA table
- Limit x sin(1/x) as x goes to infinity
- Calculus Made Simple PDF
- Find a polynomial of least degrees with real coefficients.
- domains of functions examples
- domain and range of simple linear function
- constructing a picture of a toroidal spiral
- domain and range of a quadratic function with a graph
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- finding the tensions in two ropes for a hanging object
- domain and range of a square root function with a detailed graph and explanation
- solved math problems
- parametrizing a segment in 3D over 0<=t<=1
- domain and range of an inverted quadratic function(negative leading coefficient)
- finding the domain and range of a cubic function with a graph and a detailed explanation
- concave up versus concave down
- concavity of cubic polynomial
- concavity of 1/x^2 with the second derivative
- finding the concavity of sqrt(x) with the second derivative
- finding the derivative of the absolute value of x
- find the derivative and second derivative of a vector valued function at a point including a graph of the curve velocity and acceleration in three space
- finding the derivative of |x-1| using the chain rule
- constructing a 3D coordinate system
- sketching planes in three dimensional space
- sketching a cylinder in 3D x^2+y^2=1
- deriving the distance formula in three-dimensional space
- deriving and using the equation of a sphere
- region between two spheres
- vector concepts
- adding vectors
- scalar multiplication of vectors
- multivariable calculus
- precalculus
- algebra
- calculus
- magnitude of a vector in 2D and 3D
- forming linear combinations of vectors
- unit vectors
- decomposing a vector into components from the length and angle of the vector
- dot product definition and properties
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- scalar , vector projections, work
- distance from point to line using vectors, proof of formula, with several pictures
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- solving quadratic equations by using factoring (ac method with grouping, illustrated)
- vector triple product proof and example
- torque from vector cross product
- equations of lines and planes in 3D, with examples and pictures, skew lines
- solving quadratic equations using the quadratic formula
- solving quadratic equations by completing the square, no steps skipped
- equation of a plane in 3d formula and example
- equation of a plane from three points in 3D
- where does a line in parametric form cross a plane in 3D?
- when are two planes in 3D space parallel (direction vectors are scalar multiples)
- finding the angle between two planes using their direction vectors and the dot product, finding line of intersection of two planes
- finding the distance between two skew lines in 3D space
- cylinders and quadric surfaces
- proof of Cauchy-Schwarz inequality, proof of Triangle Inequality
- vector valued functions definition, domain examples
- finding the limit of a vector-valued function, includes a graph and detailed calculations
- find parametric equations of tangent line in 3D find velocity vector and derivative of space curve
- differentiation rules for vector-valued functions with proofs
- reparametrize a curve example with a detailed explanation
- integration of vector-valued functions, examples
- arc length formula development and example for vector-valued functions
- arc length integral in 3D development with an example for a helix raparametrization by arc length example
- velocity and acceleration concepts and examples for space curves with projectile motion and tangential and normal components of acceleration using dot and cross products
- multivariable functions, domains, ranges of graphs, level curves level surfaces definitions
- when does the limit of a multivariable function exist case of a functio of two variables
- examples of level curves for different types of functions.
- example of when a limit does not exist for a function of two variables 1
- continuity of multivariable functions examples with detailed graphs
- finding the limit of a function of two variables using polar coordinates
- partial derivatives concepts graphs tangent lines examples
- max min concepts and examples in multivariable calculus
- symmetry, even /odd functions, examples with graphs and detailed explanations
- finding implicit partial derivatives examples
- tangent plane approximations part 1
- multivariable chain rule case 1 where z depends only on t with graphs
- examples of using the chain rule in calculus I
- relationship between the natural log and exponential functions and an application to derivatives
- gradient vector meaning directional derivative level curves
- max min exampls with graph in multivariable calculus
- Finding a point of intersection between two planes.
- max min examples in multivariable calculus 2
- examples of max/min questions with lagrange multipliers
- solving a system of three linear equations step by step with annotations for better understanding
- calculus III notes
- solving an inequality with three linear factors already in factored form (x+2)(x-3)(x+1) greater than or equal to 0
- solving a radical equation by squaring and solving a quadratic quadratic equation with an extranous solution
- solving a quadratic equation with complex roots detailed example with a graph
- solving a radical equation with two radicals on one side
- examples of solving equations with negative exponents
- graphing a parabola by plotting points and connecting, graphing an absolute value graph by points
- Ax+By=C facts and examples
- graphing a line by xy intercepts and making the equation of a line from two points
- simplifying experssions of the form a to the p over q
- domain /range of a relation, evaluating functions with numbers and expressions, graphical domain and range of a function, vertical line test
- examples of checking whether a function is even odd or neither
- function composition example with value plugged in
- function composition example with linear functions
- two numbers add up to 33 and the difference is 77
- solving a system of three linear equations, illustrated
- two detailed examples of variations of parameters
- write a linear function to model a situation where w is the number of weeks and g w is the value in dollars on a card
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- solving a system of three linear equations
- notes on multiplfying using foil and simple factoring factoring by grouping
- 2 by 2 example and 3 by 3 example of solving systems using Gaussian elimination
- 3 by 3 Gaussian elimination two row operations applied in one step
- using gaussian eliminination to show a system is inconstitent 3 by 3 and 2 by 2 examples with graphs of lines and planes
- detailed example of performing function transformation with reflections translations shifts
- APPLICATION OF A GAUSSIAN ELIMINATINO TO SOLVING A SYSTEM OF THREE EQUATION WITH THEATER TICKETS
- adding function, multiplying functions, dividing functions, subtrcting functions, rational functions, square root and linear function composition
- find specific combination of tofu, rice and peanuts to make a certain type of diet
- solving a linear equation
- pdf on identifying matrix columns, rows, doing matrix addition, subtraction
- solving linear equation
- solving sin squared plus cos x plus 1 equals 0 step by step with unit circle
- Analysis of Rational Function
- understanding the slope/derivative of e^x
- linear dependence/independence for functions with examples
- moving wave concepts illustrated with lots of graphs
- rational function analysis
- linear regression example found using matrices
- best linear approximation
- exponential function with a fraction in the base , horizontal asymptote, domain, range, points
- discrete compounding sample calculations, continuous compounding included.
- distance traveled by a particle found using calculus
- solving simple differential equations with initial condition built into integral
- Understanding Singularities in Complex Variables
- Using a unit vector with tension.
- detailed explanation of direction cosines
- three examples of evaluating a piece-wise defined function
- Vector Projections in 3D Space: Intuitive Explanations and Examples
- How to graph 3D Vectors
- Set Builder Notation Quiz
- Absolute Value Function and Its Transformations
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