   Chapter 1.3, Problem 109E

Chapter
Section
Textbook Problem

Proof Prove Property 1 of Theorem 1.2.

To determine

To prove: limxcbf(x)=bL, where b and c are real numbers.

Explanation

Given:

The limit,

limxcf(x)=L

Formula used:

If there exists a limit limxaf(x)=b, then for given >0 there must be a δ>0 such that,

|f(x)b|<ε|b| for the interval 0<|xa|<δ.

Proof:

If b=0, then,

limxcbf(x)=bL0=0

Thus, the property holds true for b=0.

Now, if b0, then,

Consider ε>0

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