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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

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BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

In Exercises 85-97, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

95. If f and g are both discontinuous at a, then fg must be discontinuous at a.

To determine

Whether the statement is true or false with explanation.

Explanation

The given statement is,

If f and g are both discontinuous at a , then fg must be discontinuous at a .

Assume the function is,

f(x)=g(x)={1ifx01ifx<0 (1)

Thus, the function f(x)g(x) is,

f(x)g(x)={1ifx01ifx<0

Substitute 0 for x in equation (1) to find the left hand limit of the function f(x)

limx0f(x)=limx01=1

Substitute 0 for x in equation (1) to find the right hand limit of the function f(x)

limx0+f(x)=limx0+1=1

Since, limx0f(x) and limx0+f(x) are not equal, therefore it is discontinuous at x=0

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