Write the equation of a rational function based on its graph

Graphing a rational function with two vertical asymptotes

Graphing a rational function with a slant asymptote

Decompose a vector into the sum of the projection onto another vector and the orthogonal component

Use orthogonality to express a vector as a linear combination of the basis vectors

Introductory example finding eigenvalues of a 2x2 matrix

Exponential equation, base e

Solve exponential equation - harder example

Find a basis for an eigenspace

Using cofactor expansion to compute a determinant

Find a basis for span of vectors

Basis first examples

Word problem involving angle of elevation

Using the right triangle definitions of the trig functions

Solve matrix equation using basic matrix operations

matrix transformation is a linear transformation

Linear transformations map the zero vector to zero vector

Using properties of linear transformations to compute the output

Use factor theorem to factor a degree 4 polynomial

Synthetic division and long division

Simplify trigonometric expressions using ratio identities

Simplify trig expressions using Pythagorean identities

Product Rule Examples

Quotient Rule Examples

Derivatives of trigonometric functions using Quotient Rule

Finding the second derivative examples

Chain Rule Examples

Determine whether linear transformation from R^n to R^m is one-to-one and onto

Determine whether collection of vectors is linearly independent

subtract rational expressions