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Chapter 1: Q. 1 (page 152)

Fill in the blanks to complete each of the following theorem statements:

If limx鈫�cf(x)=Landlimx鈫�cf(x)=M, then .

Short Answer

Expert verified

If limx鈫�cf(x)=Landrole="math" localid="1648282753998" limx鈫�cf(x)=M, thenL=M.

Step by step solution

01

Step 1. Given information.

The given incomplete statement is folowing.

If limx鈫�cf(x)=Landrole="math" localid="1648282783623" limx鈫�cf(x)=M, then .

02

Step 2. Explanation.

Uniqueness of Limits

The uniqueness of Limits states that if a limit limx鈫�cf(x)exists then it can be equal to one and only one number and values of a function f(x)cannot approach two different values L and M as x approaches c.

So, If localid="1648283222976" limx鈫�cf(x)=Landlimx鈫�cf(x)=M, thenlocalid="1648283490150" L=M..

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