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.