MATH 2221

1. Final Exam Review MATH 2221

2. 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!

3. Topics • Limits • Derivatives • Applications of Derivatives • Riemann Sums/Integrals

4. 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)‏

5. 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

6. 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

7. 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

8. 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.

9. Recommended Problems All problems from all semester are posted athttp://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.