MTH 8 Topics

Functions-new from old

Average and instantaneous rates of change–tangent and velocity problems

Limits

Precise definition of a limit (linear is fair game)

Continuity

Equation of a line tangent at a point

Derivatives

Limit definition of a derivative

Differentiation formulas–higher order derivatives

Derivatives of trig functions–Theorems involving limits of sin and cos

Chain rule

Implicit differentiation

Related rates

Linear approximations and differentials

Functions–intervals of increase, decrease, extrema, concavity, inflection points, etc.

Theorems–

Intermediate Value, Mean Value, Squeeze, Rolle’s, Fundamental theorem of calculus.

Limits at infinity, horizontal, vertical, and slant asymptotes

Optimization Problems

Newton’s Method

Antiderivatives

Areas and distances---Riemann Sums (if needed or or the formulas will be given)

Definite and indefinite integrals

Substitution Rules

Area between curves

Volumes (to include disk and shell methods of evaluation)

Work

Average value of a function

Be able to graph given one or more of them or other information.