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Chapter 14: Q. 21 (page 876)

Use the graph shown to determine if the limit exists. If it does, find its value.

Short Answer

Expert verified

The limit does not exist.

Step by step solution

01

Step 1. Given Information

We are given the graph and we need to determine if the limit exists and find its value.

02

Step 2. Finding the limit

We need to find the limit of the function as $x$ approaches to $3$ of $f (x)$ .

The graph of the function reaches a removable discontinuity when $x$ approaches to $3$ from the left.

From the graph, we can clearly see that $f$ approaches to $3$ from the left and to $6$ from the right as $x$ approaches to $3$ .

The value of the function from the left and right limits does not coincide.

Therefore, the limit does not exist.

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Most popular questions from this chapter

Graph each function. Use the graph to find the indicated limit, if it exists.

$\lim_{x \to - 1} f (x), f (x) = \frac{1}{x}$

$I f \lim_{x \to c} f (x) = f (c), t h e n f i s______a t__.$

In Problems 53-56, use the properties of limits and the facts that

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

$\lim_{x \to 0} \frac{\sin (2 x)}{x}$

In Problems 7– 42, find each limit algebraically.

$\lim_{x \to 2} {(3 x - 4)}^{2}$

$\lim_{x \to c} b =_____.$

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