Study Guide for Exam III
Administrative Details
The exam is Tuesday, 1 Dec from 7:30-9:30pm in room BLOC 166/169.
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
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 4.3-6.2 (asterisks indicate key formulas,
theorems, or definitions to know)
- Logarithmic Functions*
- Properties of Logarithms*
- Solving Exponential Equations using Logarithms
- Solving Logarithmic Equations
- Domain of Logarithmic Functions
- Limits of Logarithmic Functions (know graph!)
- 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.)
- Inverse Trig Functions*
- Domains of Inverse Trig Functions (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 (values IN THE DOMAIN where f'=0 or f' DNE)
- Mean Value Theorem*
- 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
- Properties of Sums (p365)
- Approximating Integrals with Riemann Sums
- Exact Integrals Using the Definition* (given 6.1 summation formulas)
Suggestions for Studying:
Return to David Manuel's Math 151 Homepage
Return to Calclab Homepage