Chapter 14: Q. 25 (page 906)

Does $\lim_{x \to 0} f (x)$ exist? If it does, what is it?

Short Answer

Expert verified

The limit $\lim_{x \to 0} f (x)$ does not exist.

Step by step solution

Step 1. Graph the function f(x)

We have been given $\lim_{x \to 0} f (x)$ .

Now let us graph the function with the help of a graphing utility.

Step 2. Determine if the limit exists.

For the limit at $0$ to exist, then $\lim_{x \to 0^{-}} f (x) = \lim_{x \to 0^{+}} f (x)$ .

Let us consider the behavior of $f (x)$ near $x = 0$ .

When we consider the limit coming from the left side, or $\lim_{x \to 0^{-}} f (x)$ , the function approaches a value of $4$ .

That is $\lim_{x \to 0^{-}} f (x) = 4$

When we consider the limit coming from the right side, or $\lim_{x \to 0^{+}} f (x)$ , the function approaches a value of $1$ .

That islocalid="1647086140473" $\lim_{x \to 0^{+}} f (x) = 1$

Since $\lim_{x \to 0^{-}} f (x) \neq \lim_{x \to 0^{+}} f (x)$ , the limit $\lim_{x \to 0} f (x)$ does not exist.

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Does $\lim_{x \to 0} f (x)$ exist? If it does, what is it?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine if the limit exists.

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Does limx→0f(x)exist? If it does, what is it?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine if the limit exists.

One App. One Place for Learning.

Most popular questions from this chapter

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Does $\lim_{x \to 0} f (x)$ exist? If it does, what is it?