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Chapter 14: Q. 20 (page 876)

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

Short Answer

Expert verified

The value is $\lim_{x \to 2} f (x) = 2$ .

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 $2$ of $f (x)$ .

The graph of the function reaches a removable discontinuity when $x$ approaches to $2$ .

From the graph, we can clearly see that $f (x)$ approaches $2$ as $x$ approaches to $2$ .

$∴ \lim_{x \to 2} f (x) = 2$

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Most popular questions from this chapter

In Problems 43-52, find the limit as $x$ approaches $c$ of the average rate of change of each function from $c$ to $x$ .

$c = 1; f (x) = \frac{1}{x}$

In Problems 13–32, use the accompanying graph of y = f(x).

Find $\lim_{x \to - 6^{+}} f (x) .$

The limit of the product of two functions equals the ____ of their limits.

In Problems 7– 42, find each limit algebraically.

$\lim_{x \to 2} \frac{x^{2} - 4}{x^{2} - 2 x} .$

Find limit algebraically: $\lim_{x \to - 3} (2 x^{3})$

See all solutions

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