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.