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Chapter 14: Q. 10 (page 889)

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

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Step. 1 Given Information

It is given in the question that limx鈫�c-f(x)=limx鈫�c+f(x), at any c.

i.e., Left hand limit is equal to right hand limit for the function f(x)atx=c.

02

Step. 2 Example

Let suppose this function,

f(x)=2x+1,x<00,x猢�0

Now, limx鈫�0-f(x)=limx鈫�0-(2x+1)=2(0)+1=1,limx鈫�0+f(x)=limx鈫�0+0=0,

We can see clearly from this example that LHL is not equal to RHL.

03

Step. 3 Conclusion

From above example it is clear that there exist atleast one function for which LHL is not equal to RHL. Therefore, the above statement is false.

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

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