Math 149 - Calculus I
Final Exam Information
Three hour, cumulative exam, self-scheduled in the finals week (December 14-December 19)
See http://www.randolphcollege.edu/x13440.xml for procedures about self-scheduled exams.
The final exam is cumulative with about 60% from the material covered after the third exam (from section 3.8 to section 4.6) and 40% from earlier material.
Topics
Limits and Continuity
Idea behind limit (Left limit, right limit; when does a limit exists , when does it not exist)
Evaluating limits
Dividing-out technique( factor and simplify)
Rationalizing technique
Squeeze (Sandwich) theorem
Limit of piecewise functions
The Greatest
integer function
Limits at infinity (horizontal asymptotes)
When is a function continuous? When is it not continuous?
Intermediate Value Theorem
Derivatives
Formal definition of derivative
Equation of a tangent line
Rules of differentiation (basic derivatives, product rule, quotient rule, chain rule)
Implicit differentiation
Rolle's Theorem and Mean Value Theorem
Definition of local (relative) maximum minimum, absolute (global) maximum minimum
Finding local max/min (First derivative test and second derivative test)
Finding absolute max/min of a continuous function on a closed interval
Finding absolute max/min of a continuous function on an open interval
Definition of an inflection point
Finding inflection point(s)
Applications of Derivatives
Related rate problems
Optimization problems (maximize or minimize functions subject to a constraint)
Approximating zeros of a function (Newton's method)
Estimating the value of a function (differentials and tangent line approximation)
Error in a computation (differentials)
Curve sketching
Domain of the function
x,y intercepts of the function
Sign of the function (sign chart for f(x) )
Vertical/horizontal asymptotes of the function
Intervals where the function increases/decreases (sign chart for f'(x))
Local max/min points of a function
Intervals where the function is concave up/down (sign chart for f"(x))
Points of inflection
Putting them all together
Integrals
Indefinite integrals (Antiderivatives)
Differential equations with an initial value
Applications to
acceleration, speed, position
Area under a curve
Sigma notation
Upper
estimate/lower estimate by rectangles
Definite integrals (Riemann Sums)
Relation of the
Riemann Sum to the area
Fundamental theorem of Calculus I
Fundamental theorem of Calculus II
Evaluating integrals by substitution
Trapezoidal Rule
Simpson's Rule
Practice Problems
Solving ONLY these problems is NOT sufficient to do well in the exam! You should also go over class notes, examples in class, previous quizzes, exams, and homework problems. Pay extra attention to the problems that you had difficulty solving. Learn and understand how to solve them.
Textbook: Calculus by Larson, Hostetler, Edwards, Eighth Edition
Review Exercises for Chapter 1 page 91
Odd problems among 5, 11-22, 31-36, 37-47, 51-70
Review Exercises for Chapter 2 page 158
Odd problems among 1-4, 9, 10, 11, 12, 15-30, 31, 33, 37, 41-54, 55-58, 61-82, 99,101-106,109,110,111,113
Review Exercises for Chapter 3 page 242
Problems 1,3,5,9,11,15,17,19,23,25,27,29,33,35,37,39,41,43,49,51,53,55,57,59,61,63,65,69,79,81,83,85,87
Review Exercises for Chapter 4 page 316
Problems 3,5,7,9,13,15,17,19,21,23,27,29,37,41,43,45,47,49,51,53,55,57,59,61,67,69,71,73,75,77,79,81,83,85,87,91,93,95,97(do the Trapezoidal Rule only)
If you finish the odd problems and want to practice more, you can work on the even-numbered problems.