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Chapter 3: Q. 24 (page 310)
Calculate each of the limits in Exercises 21–48. Some of these limits are made easier by L’Hopital’s rule, and some are not
The value of the given limit
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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.
Use a sign chart for to determine the intervals on which each function is increasing or decreasing. 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.
Use a sign chart for to determine the intervals on which each function is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.
role="math" localid="1648368106886"
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f(0) = 5;
f(−2) = −3 and f '(−2) = 0;
f '(1) does not exist;
f' is positive only on (−2, 1).
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