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Chapter 1: Q. 47 (page 149)

Calculate each limit in Exercises 35–80.
$\lim_{x \to 0} \frac{x}{x^{2} - x}$

Short Answer

Expert verified

The limit is - 1.

Step by step solution

01

Step 1. Given Information:

Given expression: $\lim_{x \to 0} \frac{x}{x^{2} - x}$

We want to find the limit of given expression.

02

Step 2. Solution:

Take x common form denominator we get:

$\lim_{x \to 0} \frac{x}{x^{2} - x} = \lim_{x \to 0} \frac{x}{x (x - 1)} = \lim_{x \to 0} \frac{1}{x - 1}$

Now put limit we get

$\lim_{x \to 0} \frac{1}{x - 1} = \frac{1}{0 - 1} = - 1$

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Most popular questions from this chapter

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

What are punctured intervals, and why do we need to use them when discussing limits?

Calculate each of the limits:

$\lim_{x \to 0} \frac{1}{s e c^{- 1} x}$ .

Calculate each of the limits:

$\lim_{h \to 0} \frac{{(3 + h)}^{2} - 3^{2}}{h}$ .

Calculate each of the limits:

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

See all solutions

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