MATH 2221

Final Exam Review

When, Where, What?

Wednesday, December 9th at 8:00-11:00AM.

Jolly Room as always.

Sit spaced out throughout the classroom.

Don’t forget to bring a calculator!

And eat breakfast first!

Topics

Limits

Derivatives

Applications of Derivatives

Riemann Sums/Integrals

Limits(2.2)-Definition of a limit, existence of limits, right

and left-hand limits, infinite Limits

(2.3)-Limit laws (sum of limits=limit of sums, etc.), Direct substitution property, Squeeze Theorem

(2.4)-Continuity 3 rules: f(a) defined, limit of f(x) exists, and limit

of f(x) as x a is f(a) f is continuous at a right and left-hand continuity, continuity on an

interval, functions that are continuous everywhere, continuity of function compositions, Intermediate Value Theorem (IVT)

Limits, Cont.(2.5)-Limits involving infinity (vertical and

horizontal asymptotes), infinite limits

(2.6)-Tangents, velocities, derivatives

(2.7)-Derivative of a function at a point “a”, derivative as a function (defn. on p. 146), notations, differentiable, non differentiable points, 2nd derivatives

(2.8)-Information on f from f', antiderivatives, increasing/decreasing, local max/min, concavity, points of inflection

Derivatives(3.1)-Derivatives of polynomials and

exponentials, derivation rules (derivative of the sums is the sum of the derivatives)

(3.2)-Product and quotient rules

(3.3)-Derivatives of trigonometric functions

(3.4)-Chain Rule

(3.5)-Implicit Differentiation, find eqn of a tangent line implicitly, find second derivative implicitly

(3.7)-Derivatives of logarithmic functions

Applications of Derivatives

(4.1)-Related rates

(4.2)-Critical numbers, absolute/local maximum and minimum values

(4.3)-Increasing/decreasing, first/second derivative test, concavity

(4.5)-Indeterminate forms and l'Hospital's Rule

(4.6)- Word problems, using concepts from 4.3

Riemann Sums/Integration

(5.1)-Areas and Riemann Sums, right-hand, left-hand, and midpoint Riemann sums, summation notation

(5.2)-Definite integrals, write integral as a limit of sums, properties of integrals

(5.3)-Evaluation of definite (and indefinite) integrals, more properties

(5.4)-FToC! Use both parts well.

(5.5)-Substitution – we didn’t spend enough time on it. We’ll cover this well in Calculus 2.

Recommended Problems

All problems from all semester are posted at

http://home.lagrange.edu/sernstberger/calculus/MATH2221_F09.html

I highly recommend that you work these problems, as well as other problems worked in class, and given on tests/quizzes/homework.