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Chapter 1: Q. 29 (page 135)

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to 0} (x^{2} - 1)$ .

Short Answer

Expert verified

The value of $\lim_{x \to 0} (x^{2} - 1)$ is, $- 1$ .

Step by step solution

01

Step 1. Given information

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

02

Step 2. The limit is calculated as below:

$\lim_{x \to 0} (x^{2} - 1) = \lim_{x \to 0} (x^{2}) - \lim_{x \to 0} (1)$ [Sum rule]

$= {(0)}^{2} - 1 = 0 - 1 = - 1$

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

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