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Chapter 1: Q. 29 (page 88)

Consider the limit values below:
$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = - 1 and f (2) = 2$
The strategy is to sketch the graph of the function having the above limit values

Short Answer

Expert verified

The graph obtained is

Step by step solution

Step 1. Given

The given limit values are

$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = - 1 and f (2) = 2$

Step 2. Graph obtained

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Most popular questions from this chapter

For each limit statement in Exercises $41 - 44$ , use algebra to find $δ$ or $N$ in terms of $ε$ or $M$ , according to the appropriate formal limit definition.

$\lim_{x \to \infty} \frac{x - 1}{x} = 1$ , find $N$ in terms of $ε$ .

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

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

$\lim_{x \to 0} \frac{\sin x}{\cos x}$

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

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Consider the limit values below:limx→2-f(x)=2,limx→2+f(x)=-1andf(2)=2The strategy is to sketch the graph of the function having the above limit values

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph obtained

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Consider the limit values below:
$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = - 1 and f (2) = 2$
The strategy is to sketch the graph of the function having the above limit values