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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If f(x) > 1 for all and lim x 0 f ( x ) exists, then lim x 0 f ( x ) > 1.

To determine

Whether the statement, “If f(x)>1 for all x and limx0f(x) exists, then limx0f(x)>1” is true or false.

Explanation

Reason:

The given statement is false since the below example disproves the given statement.

Let f(x)={x4+1ifx0 3if x=0

Here, for any x in , f(x)>1 and if x0, f(x)=x4+1 is a polynomial and it is continuous everywhere on its domain

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