Limits

Limit of a function, limit from the left, limit from the right, improper limits, rules for calculating limits, continuous function

Derivatives

Tangent line to and dervative of a function at a point, derivative as a function, calculating simple derivatives, higher-order derivatives

Calculating derivatives

Table of basic derivatives, derivative of the sum, difference, product and quotient of two functions, derivative of a composite function, derivative of an inverse function, derivatives of hyperbolic trigonometric functions and their inverses

Taylor theorem

Defintion of a Taylor polynomial to a function, the remainder of a Taylor polynomial, MacLaurin polynomial, MacLaurin polynomials of exp(x), sin(x), cos(x), ln(x+1), using MacLaurin polynomial to calculate values of functions

Continuous functions on closed interval

Properties of a continuous function on a closed interval,Rolle's theorem, mean value theorem

L'Hospital's rule

Finding limit of functions of the 0/0, infinity/infinity types, L'Hospital's rule, other limit types to which L'Hospital's rule can be applied

Extremes

Derivatives of increasing and decreasing functions, functions bending up and functions bending don and their second derivatives, inflexion points, local minima nd maxima of functions, necessary and sufficient conditions for a function to have a local maximum/minimum

Sketching graphs

Asymptotes to the graph of a function, asymptotes with and without slope, procedure for sketching the graph of a function