Using scheme to compute derivatives and integrals.
Graphing guidelines using first derivative test and concavity test (aka second derivative test).
Volume and area using integration techniques.
Applications of the derivative to optimize functions.
Rolle's theorem and the Mean value theorem (MVT).
Finding vertical tangent lines of a function.
Some word problems involving rates and derivatives.
Solving for equations of tangent lines involving specific points on a graph.
Determining maximum error, average and percentage error using differentials.
Solving problems with the derivative and increments of x, involving linear approximation.
Proofs for the product rule and quotient rule when finding the derivative.
Proof of trigonometric derivatives using the Limit Definition of the Derivative.
Some different problems using the derivative.
Use the derivative to find the instantaneous velocity of a function.
The Derivative, tangent lines, and rates of change.
Limits that lead to the discovery of a vertical asymptote.
Solving limits using the Sandwich Theorem, or Squeeze Theorem.
Explore continuous functions with the intermediate value theorem.
Solving limits with unbounded values of infinity.
Techniques for finding the derivative using implicit differentiation.
How to make a proof for a Limit of a function using delta and epsilon.
The precise definition of the Limit of a function.