Q. 2 Fill in the blanks to complete e... [FREE SOLUTION]

Chapter 1: Q. 2 (page 152)

Fill in the blanks to complete each of the following theorem statements:
$\lim_{x 鈫� c} f (x) = L$ if and only if $\lim_{x 鈫� c^{-}} f (x) =$ and $\lim_{x 鈫� c^{+}} f (x) = .$

Short Answer

Expert verified

$\lim_{x 鈫� c} f (x) = L$ if and only if role="math" localid="1648285012992" $\lim_{x 鈫� c^{-}} f (x) = L$ and $\lim_{x 鈫� c^{+}} f (x) = L .$

Step by step solution

Step 1. Given information.

The given incomplete statement is the following.

$\lim_{x 鈫� c} f (x) = L$ if and only if $\lim_{x 鈫� c^{-}} f (x) =$ and $\lim_{x 鈫� c^{-}} f (x) = .$

Step 2. Explanation.

If a limit $\lim_{x 鈫� c} f (x)$ Exists, then the Left and Right Limits Must Exist and Be Equal.

So $\lim_{x 鈫� c} f (x) = L$ if and only if $\lim_{x 鈫� c^{-}} f (x) = L$ and $\lim_{x 鈫� c^{-}} f (x) = L .$

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91影视

Fill in the blanks to complete each of the following theorem statements:
$\lim_{x 鈫� c} f (x) = L$ if and only if $\lim_{x 鈫� c^{-}} f (x) =$ and $\lim_{x 鈫� c^{+}} f (x) = .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

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91影视

Fill in the blanks to complete each of the following theorem statements:limx鈫�cf(x)=Lif and only if limx鈫�c-f(x)=andlimx鈫�c+f(x)=.

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

Geometry

Applied Mathematics

Decision Maths

Discrete Mathematics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
$\lim_{x 鈫� c} f (x) = L$ if and only if $\lim_{x 鈫� c^{-}} f (x) =$ and $\lim_{x 鈫� c^{+}} f (x) = .$