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Chapter 1: Q. 28 (page 153)

Find the limit by hand.
$\lim_{x 鈫� 0} \frac{x^{2}}{e^{x} - 1}$

Short Answer

Expert verified

On solving the limit, we get, $0$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\lim_{x 鈫� 0} \frac{x^{2}}{e^{x} - 1}$

02

Step 2. Solve the given limit.

Rewriting the expression,

$= \lim_{x 鈫� 0} [(\frac{x}{e^{x} - 1}) x]$

Using the product rule,

$= \lim_{x 鈫� 0} \frac{x}{e^{x} - 1} \lim_{x 鈫� 0} x$

As $\lim_{h 鈫� 0} \frac{h}{e^{h} - 1} = 1$ ,

$= 1 (0) = 0$

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Most popular questions from this chapter

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x}))$

Use what you know about one-sided limits to prove that a function $f$ is continuous at a point $x = c$ if and only if it is both left and right continuous at $x = c$ .

Calculate each of the limits:

$\lim_{h 鈫� 0} \frac{{(- 1 + h)}^{3} - {(- 1)}^{3}}{h}$ .

$\lim_{x 鈫� 0} (\frac{e^{x} - 1}{e^{2 x} + 2 e^{x} - 3})$

For each of the following sign charts, sketch the graph of a function f that has the indicated signs, zeros, and discontinuities:

See all solutions

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