MATH 2221 Final Exam Review

When, Where, What? Wednesday, December 9 th 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, 2 nd 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 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.