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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.

93. If f is continuous for all x ≠ 0 and f(0) = 0, then lim x 0 f ( x ) = 0 .

To determine
Whether the statement is true or false with explanation.

Explanation

The given statement is,

If f is continuous for all x0 and f(0)=0 , then limx0f(x)=0 .

The function will be continuous when the value of left hand limit and the value of right hand limit is equal to the value of the function at that point and value of that function should satisfy that point.

A function f is continuous at x=a when it follows the following three conditions,

(1) f(a) is defined.

(2) limxaf(x) exists.

(3) limxaf(x)=f(a) . The value of limxaf(x)g(x) is,

Assume the function is,

f(x)={3xifx02x+1ifx>0 (1)

Substitute 0 </

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