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Chapter 3: Q. 80 (page 311)

Calculate the limits $\lim_{x \to \infty} e^{- x} \ln (x)$

Short Answer

Expert verified

The limits of given function $\lim_{x \to \infty} e^{- x} \ln (x)$ is 0

Step by step solution

01

Step 1. Given information

The given information is $\lim_{x \to \infty} e^{- x} \ln (x)$

02

Step 2. Calculate the limits

$\lim_{x \to \infty} e^{- x} \ln (x) = \lim_{x \to \infty} \frac{\ln (x)}{e^{x}}$

Using the L hospitals rule

$= \lim_{x \to \infty} \frac{\frac{1}{x}}{e^{x}} = \lim_{x \to \infty} \frac{1}{x e^{x}} = 0$

The limit is 0

03

Step 3. The solution

The limit of given function is 0

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Most popular questions from this chapter

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.

$f (x) = x^{3} + 4 x^{2} + 4 x - 5$

For the graph of f in the given figure, approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.

For the graph of f in the given figure, approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.

Find the possibility graph of its derivative f'.

For the graph of f in the given figure , approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points .

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