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Chapter 1: Q. 54 (page 88)

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to - 1} (x^{3} - 2)$

Short Answer

Expert verified

The value of $\lim_{x \to - 1} (x^{3} - 2) = - 3$ and graph is

Step by step solution

01

Step 1. Given information.

The given function is $\lim_{x \to - 1} (x^{3} - 2)$ .

02

Step 2. Graph of the function.

The graph of the function is,

$A s x \to - 1, f (x) = - 3 T h e r e f o r e, \lim_{x \to - 1} (x^{3} - 2) = - 3$

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Most popular questions from this chapter

In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

$f (x) = \{\begin{cases} (x - 3), i f x < 3 \\ - (x - 3), i f x ⩾ 3 \end{cases} .$

Write delta-epsilon proofs for each of the limit statements in Exercises $47 - 60 .$

$\lim_{x \to 5^{+}} \sqrt{x - 5} = 0$

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

$\lim_{x \to 2} (x^{2} - 4 x + 6) = 2$

Write each of the inequalities in interval notation:

$0 < | x - 2 | < 0.1$

Write a delta–epsilon proof that proves that f is continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.

$f (x) = x^{- 1}$

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