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– Midterm 2 Review
Midterm 2 will cover sections 2.6-2.9, 3.1-3.6, 3.8-3.9, and 4.1-4.2.
No calculators will be allowed for this midterm.
You may bring a 4x6 index card of notes (on both sides, if you want) to use
as a reference. Make sure it’s truly a 4x6 index card and not something that
closely resembles a 4x6 index card. If you need one, I can provide one for
you.
Course Objectives covered on this Exam:
• Use limits to discuss the continuity of a function in one variable and identify
asymptotes of a function in one variable.
• Compute derivatives of algebraic and trigonometric functions in one variable
both explicitly and implicitly.
• Analyze a graph using understanding of derivatives and limits.
• Apply knowledge of derivatives to solve problems (linear approximation,
related rates, optimization).
• Compute indefinite integrals of some algebraic and trigonometric functions
in one variable.
Topics
• Higher-Order Derivatives
• Implicit Differentiation
• Related Rates
• Differentials/Approximations
• Analyze graph
o domain
o asymptotes
 Find vertical and horizontal asymptotes using limits.
 Find oblique asymptotes of rational functions using long division.
o critical points (endpoints, stationary, and singular points)
o increasing/decreasing (1st derivative sign line)
o max/min points or values (global vs local)
o concavity (2nd derivative sign line)
o inflection points
o sketch graph
• Optimization problems
• MVT for Derivatives
• Indefinite Integrals (Antiderivatives)
• Separable Differential Equations
• Special Sum formulas and Area
• Definition of Definite Integral
Midterm Review Problems:
Section 2.10 – Concepts Test (p. 147-148) #16, 17, 18, 23, 27, 28, 32, 36, 37
Sample Test (p. 148-149) #10, 15, 28, 29, 31, 35-44, 49, 50
Section 3.10 – Concepts Test (p. 209-210) #4-10, 13, 15-19, 22, 24, 27, 41, 42
Sample Test (p. 210-213) #1-37 odd, 40-43, 45, 47, 48, 53-75 odd
Section 4.7 – Concepts Test (p. 270-271) #1, 3, 8, 9, 16, 40, 42
Sample Test (p. 271-273) #18-22
I would also recommend using the Quizzes 5-10 and past homework assignments
when reviewing for the exam.