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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.

Let f be a function such that lim x 0 f ( x ) = 6. Then there exists a positive number δ such that if 0 < | x | < δ, then | f(x) – 6| < 1.

To determine

Whether the statement, “Let f be a function such that limx0f(x)=6. Then there exists a number δ such that if 0<|x|<δ, then |f(x)6|<1” is true or false.

Explanation

Definition used:

“Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then, the limit of f(x) as x approaches a is L, limxaf(x)=L if for every number ε>0 there is a number δ>0 such that if 0<|xa|<δ then |f(x)L|<ε”.

Reason:

Given that, f be a function such that limx0f(x)=6.

Here, a=0 and L=6

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