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Posted on March 31, 2024March 31, 2024 by tom

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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
c sharp interview quizzes page
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
convert r = 2 sin(theta) to rectangular form
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.
e to the log base x of 2 equals 5
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 a if x=1 in |x| = ln(1/(ax))
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 solution to x^2-4|x|=0
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
Geometry Challenge: Calculating Radius Increase in Surface Intersections
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 Find a Point P that Makes Line PQ Perpendicular to Line CD – Step-by-Step Geometry Solution
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 c sharp job interview quizzes
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 quiz questions page from 4 28 2024
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.
Solve x² + 5|x| + 6 = 0
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
tetris game
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
translations, rotations and dilations of shapes guide lines for using a protractor and ruler
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 Curvature Through the Laplacian: How Deviation from Averages Reveals Function Behavior
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
updated tetris game with newer features
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 the allowed values of a in ln(2x+y)=a
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 will be the impact of adding the next term . In other words, if we add one more term(what is it? ) , where will the next curve go , say, at x=1.5?
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 derivative of ln(2x+y)=a
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 extra solution come from?
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
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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
finding the domain and range of a square root function with a graph
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
directions cosines for a vector in 3D
scalar , vector projections, work
distance from point to line using vectors, proof of formula, with several pictures
deriving the formula for finding the cross product of two vectors and vector product properties and applications with pictures
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
- application of a system of three linear equations to investments
- examples of solving systems of equations with three variables
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
sample solutions for 1.5 math 201 mercy fall 2021 average rate of change function graph comparing average rates of change
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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