Chapter 1: Q. 1 (page 152)

Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} f (x) = M$ , then .

Short Answer

Expert verified

If $\lim_{x \to c} f (x) = L$ androle="math" localid="1648282753998" $\lim_{x \to c} f (x) = M$ , then $L = M .$

Step by step solution

Step 1. Given information.

The given incomplete statement is folowing.

If $\lim_{x \to c} f (x) = L$ androle="math" localid="1648282783623" $\lim_{x \to c} f (x) = M$ , then .

Step 2. Explanation.

Uniqueness of Limits

The uniqueness of Limits states that if a limit $\lim_{x \to c} f (x)$ 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" $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} f (x) = M$ , thenlocalid="1648283490150" $L = M .$ .

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Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} f (x) = M$ , then .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

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Fill in the blanks to complete each of the following theorem statements:If limx→cf(x)=Landlimx→cf(x)=M, then .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} f (x) = M$ , then .