General Information
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The exam will be held on Thursday, November 1, from 5:30pm to 7:00pm, in Smith Labs 154.
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Plan to arrive a few minutes early to allow time to distribute the exams.
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The exam will cover material from sections 2.3, 2.4, 2.5, 2.6 , 2.7, 2.8, 3.1, 3.2, and 3.3 in the text.
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Cell-phones should be turned OFF for the duration of the exam.
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You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
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This is a closed-book exam. No books or notes may be used during the exam.
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You will be expected to show all of your work. A correct answer with insufficient justification
may not receive full credit.
Topics
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Limit Laws. (2.3) Know how to evaluate limits of sums, differences, products, quotients, and roots of functions with known limits.
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Continuity. (2.4) Know the definition of continuity (page 76), as well as one-sided continuity (page 77). Be able to identify where a given function is continuous or discontinuous, and know the three types of discontinuities.
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Evaluating Limits Algebraically. (2.5) Know how to use algebra to evaluate limits that involve indeterminate forms such as 0/0.
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Trigonometric Limits. (2.6) Know how to use the Squeeze Theorem to evaluate limits. Know the two basic trigonomteric limits (Theorem 2 on page 90), and be able to use them to evaluate other limits involving trigonometric functions.
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Limits at Infinity. (2.7) Know how to compute limits of a given function as x approached positive or negative infinity. Know what these limits tell us about the graph of the function.
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Intermediate Value Theorem. (2.8) Know the statement of the Intermediate Value Theorem (page 100). Know how to use the IVT to prove that a given equation has a solution or solutions. Know how to use the bisection method to approximate a solution to a given equation.
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Definition of the Derivative. (3.1) Know the limit definition of the derivative of a function at a point a (page 114). Be able to use the definition to compute the derivative of a function at a given point. Know how to find the equation of the tangent line to the graph of a function at a given point.
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Derivative Formulas. (3.2 and 3.3) Know all the basic derivative formulas: Theorems 1-5 in 3.2, and the product rule and quotient rule in 3.3. Also know the formula for the derivative of bx. Know that differentiability implies continuity (but not vice versa). Also know the relation between the derivative of a function f and the graph of f (see Examples 5 and 6 in 2.2).
Preparing for the Exam
The exam will consist of questions similar to those assigned on the worksheets (6 through 12), quizzes (4 through 6) and WebAssign (Assignments 4 through 6). Be sure you are familiar with how to solve these types of problems. Here are a some additional problems from the Chapter Review sections to use for practice. Solutions to the odd-numbered exercises are in the back of the text.
Chapter 2 Review, p. 110
Exercises 11-54, 57-64, 68, 71-74.
Chapter 3 Review, p. 189
Exercises 5-12, 17-19, 27, 29-34, 41, 55-56, 67-68, 85-87, 91.
