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Chapter 14: Q. 26 (page 906)

Is f continuous at 0?

Short Answer

Expert verified

f(x)is not continuous atx=0.

Step by step solution

01

Step 1. Graph the function f(x)

Let us graph f(x)with the help of a graphing utility.

02

Step 2. Determine f(x) is continuous at 0

For a function to be continuous atx=c, then the function must be defined at x=candlimx鈫�c-f(x)=limx鈫�c+f(x)=f(c).

Let us consider the behavior of f(x)near x=0.

When we consider the limit coming from the left side, the function approaches a value of 4.

That islimx鈫�0-f(x)=4

When we consider the limit coming from the right side, the function approaches a value of 1.

That islimx鈫�0+f(x)=1

Sincelimx鈫�0-f(x)鈮�limx鈫�0+f(x),f(x)is not continuous atx=0.

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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.

limx鈫�0f(x),f(x)=1ifx<0-1ifx>0

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True or False For any function f, and any real number c,limx鈫�c-f(x)=limx鈫�c+f(x).

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