Chapter 14: Q. 29 (page 889)

In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at 0?

Short Answer

Expert verified

The answer is Yes. The function is continuous at 0.

Step by step solution

Step. 1 How to check continuity?

For a function to be continuous its LHL = RHL = f(c) at the point $x = c$ .

Step. 2 Calculating LHL, RHL and f(c).

Firstly we calculate $f (0)$ which is equal to 3 as given in the graph.

Now, we calculate LHL which is,

$\lim_{x \to 0^{-}} f (x) = 3$ .

Finally we see RHL which is,

$\lim_{x \to 0^{+}} f (x) = 3$ .

From here we can see that $L H L = R H L = f (0) \lim_{x \to 0^{-}} f (x) = \lim_{x \to 0^{+}} f (x) = f (0) = 3$

So, all the conditions to check continuity passes. That's why, the function is continuous at $x = 0$ .

And from the graph itself we can clearly see that we don't have to pick our pencil up the paper when we move through $x = 0$ which is also a method to check whether the function is continuous or not.

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In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at 0?

Short Answer

Step by step solution

Step. 1 How to check continuity?

Step. 2 Calculating LHL, RHL and f(c).

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In Problems 13–32, use the accompanying graph of y = f(x).Is f continuous at 0?

Short Answer

Step by step solution

Step. 1 How to check continuity?

Step. 2 Calculating LHL, RHL and f(c).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at 0?