Study Guide for Exam III



Administrative Details
  • The exam is Tuesday, 25 Nov from 7:30-9:30pm in room HECC 207. Seating charts will be posted by 7:15pm outside the doors.
  • The exam will consist of two parts. Part I will have multiple-choice answers; mark the letter of the best choice on your Scantron. No work will be graded and no partial credit will be given. Part II will consist of workout problems. All answers must be justified with appropriate algebraic work. Partial credit will be given for appropriate work shown.
  • Calculators are not allowed at any time on the exam.
  • Bring: Writing Utensil, Picture ID (NOTE: you will be using the back side of a prior scantron!)
    Students without a picture ID may have to bring a picture ID to my office and sign a document allowing them to pick up their exam and have the grade recorded!

    Summary of Topics 4.4-6.4 (asterisks indicate key formulas, theorems, or definitions to know)

  • Derivative of ln x*
  • Chain Rule with Logarithmic Functions
  • Logarithmic Differentiation
  • Derivatives of Exponential/Logarithmic Functions in Other Bases*

  • Exponential Growth and Decay (y' = ky AND y = Cekt)*
  • Applications (Compound Interest, Radioactive Decay, Population Growth, Salt Water Tanks, Newton's Law of Cooling, etc.)

  • Domains of Inverse Trig Functions (ITF)*
  • Computing ITF
  • Derivatives of ITF*
  • Derivations of ITF Derivatives (Reference Triangles)
  • Limits of ITF

  • L'Hospital's Rule*
  • Indeterminate Forms (0/0, inf/inf)
  • Indeterminate Forms (0*inf, inf-inf): Rewrite as quotient
  • Indeterminate Forms (inf^0, 1^inf, 0^0 etc)): Apply log and rewrite as quotient
            (Remember to apply exponential when you are done!)

  • Graphical Interpretation of First Derivative*
  • Graphical Interpretation of Second Derivative*
  • Graph of Function Given Graph of Derivative
  • Graph of Derivative Given Graph of Function
  • Sketching Graph of Function given information about f, f', and f''

  • Absolute Extrema
  • Relative Extrema
  • Extreme Value Theorem
  • Critical Numbers (f'=0 or f' DNE)

  • Increasing/Decreasing/First Derivative Test
  • Concavity
  • Inflection Points
  • Second Derivative Test (determines Rel Max/Min)*

  • Applied Max/Min Problems-Set up Geometric Problems

  • Antiderivatives-General (+C)*
  • Specific Antiderivative Given Initial Data
  • Acceleration/Velocity/Position
  • Acceleration/Velocity/Position-Vectors

  • Sigma Notation

  • Approximating Integrals with Riemann Sums
  • Exact Integrals Using the Definition* (given 6.1 summation formulas)
  • Properties of Definite Integrals
  • Computing Integrals Using Area

  • Fundamental Theorem of Calculus, pt 1
  • Fundamental Theorem of Calculus, pt 2

    Suggestions for Studying:

  • Read your textbook, including all Examples
  • Read your notes from lecture, including all Examples
  • Suggested Homework Problems
  • Past 151 Common Exams (Fall 2003 Monday 24 Nov, Spring 2003 Tuesday 25 Nov)
  • Week in Review/Night Before Drill via streaming video online
  • Live Week in Reviews Tuesdays 7-9pm BLOC 165

    Return to David Manuel's Math 151 Homepage


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