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Chapter 14: Q. 29 (page 889)

In Problems 13鈥�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

01

Step. 1 How to check continuity? 

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

02

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,

limx鈫�0-f(x)=3.

Finally we see RHL which is,

limx鈫�0+f(x)=3.

From here we can see that LHL=RHL=f(0)limx鈫�0-f(x)=limx鈫�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=0which is also a method to check whether the function is continuous or not.

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Most popular questions from this chapter

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

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