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Chapter 3: Q. 14 (page 313)

If $\lim_{x \to c} \ln (f (x)) =____$ , then $\lim_{x \to c} f (x) = 0$

Short Answer

Expert verified

If $\lim_{x \to c} \ln (f (x)) = - \infty$ , then $\lim_{x \to c} f (x) = 0$

Step by step solution

01

Step 1. Given information

The given statement is,

If $\lim_{x \to c} \ln (f (x)) =___$ , then^{$\lim_{x \to c} f (x) = 0$}

02

Step 2. Fill in the blanks

The given statement is a theorem

That is,

If $\lim_{x \to c} \ln (f (x)) = - \infty$ , then $\lim_{x \to c} f (x) = 0$ .

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Most popular questions from this chapter

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

Use a sign chart for $f^{'}$ to determine the intervals on which each function $f$ is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648368106886" $f (x) = s i n (\frac{π}{2} x)$

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.

Find the critical points of the function

$f^{'} (x) = \frac{(x - 1) (x - 2)}{x - 3}$

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

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