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Chapter 3: Q. 41 (page 311)
Calculate each of the limits in Exercises 15–20 (a) using
L’Hopital’s rule and (b) without using L’H ˆ opital’s rule.
a
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For each set of sign charts in Exercises 53–62, sketch a possible graph of f.
Restate Theorem 3.3 so that its conclusion has to do with
tangent lines.
Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.
Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.
For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.
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