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Simulations
Ohm’s law simulation
Wave on a string simulation
Completing an ANOVA table
AP Calculus BC solved problem
Calculus Made Simple PDF
solved calculus bc math problems on arc length, differential equations and the integral of the second derivative
Limit x sin(1/x) as x goes to infinity
solved math problems
algebra
-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)
240 is 30% of what number?
A rectangular room is 3 times as long as it is wide
age problem algebra | algebra age problem
age problem involving number of years ago ages were equal
solving quadratic equations by using factoring (ac method with grouping, illustrated)
solving quadratic equations using the quadratic formula
solving quadratic equations by completing the square, no steps skipped
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
two numbers add up to 33 and the difference is 77
simplifying experssions of the form a to the p over q
precalculus
domain and range of a square root function with a detailed graph and explanation
finding the domain and range of a square root function with a graph
domain and range of a quadratic function with a graph
domain and range of simple linear function
Find a polynomial of least degrees with real coefficients.
domains of functions examples
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
solving rational equations examples with graphs
detailed examples of solving radical equations ,including using graphs
symmetry, even /odd functions, examples with graphs and detailed explanations
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
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
solving a system of three linear equations step by step with annotations for better understanding
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
notes on multiplfying using foil and simple factoring factoring by grouping
detailed example of performing function transformation with reflections translations shifts
adding function, multiplying functions, dividing functions, subtrcting functions, rational functions, square root and linear function composition
calculus
relationship between the natural log and exponential functions and an application to derivatives
where are the graphs of x^2 and x^3 concave up/down?
concave up versus concave down
concavity of 1/x^2 with the second derivative
concavity of cubic polynomial
finding the concavity of sqrt(x) with the second derivative
finding the derivative of the absolute value of x
finding the derivative of |x-1| using the chain rule
examples of using the chain rule in calculus I
multivariable calculus
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
examples of inequalities in 3D
vector concepts
adding vectors
scalar multiplication of vectors
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
finding the tensions in two ropes for a hanging object
dot product definition and properties
proof of Cauchy-Schwarz inequality, proof of Triangle Inequality
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
vector triple product proof and example
torque from vector cross product
equations of lines and planes in 3D, with examples and pictures, skew lines
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
derive the formula for the distance between a point and a plane in 3D space
finding the distance between two skew lines in 3D space
cylinders and quadric surfaces
vector valued functions definition, domain examples
finding the limit of a vector-valued function, includes a graph and detailed calculations
identify the curve defined by a vector-valued function
constructing a picture of a toroidal spiral
concepts behind vector-valued function derivatives and an example
parametrizing a segment in 3D over 0<=t<=1
find parametric equations of tangent line in 3D find velocity vector and derivative of space curve
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
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
examples of level curves for different types of functions.
example of limits in multivariable calculus one exists and one doesn’t exist
when does the limit of a multivariable function exist case of a functio of two variables
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
Understanding second partial derivatives with graphs
finding implicit partial derivatives examples
tangent plane approximations part 1
multivariable chain rule case 1 where z depends only on t with graphs
gradient vector meaning directional derivative level curves
max min concepts and examples in multivariable calculus
max min exampls with graph in multivariable calculus
max min examples in multivariable calculus 2
examples of max/min questions with lagrange multipliers
Finding a point of intersection between two planes.
solving a system of three linear equations, illustrated
calculus III notes
solving a system of three linear equations
examples of solving systems of equations with three variables
application of a system of three linear equations to investments
3 by 3 Gaussian elimination two row operations applied in one step
2 by 2 example and 3 by 3 example of solving systems using Gaussian elimination
using gaussian eliminination to show a system is inconstitent 3 by 3 and 2 by 2 examples with graphs of lines and planes
APPLICATION OF A GAUSSIAN ELIMINATINO TO SOLVING A SYSTEM OF THREE EQUATION WITH THEATER TICKETS
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
two detailed examples of variations of parameters
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
How do we know that ∑ₙ₌₀^∞ rⁿ is the same as ∑ₙ₌₁^∞ rⁿ⁻¹?
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