Chapter 1: Q 4. (page 86)

If $\lim_{x \to 0^{+}} f (x) = - 2$ , $\lim_{x \to 0^{-}} f (x) = 3$ , and $f (0) = - 2$ , what can you say about $\lim_{x \to 0} f (x)$ ?

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

It is given that $\lim_{x \to 0^{+}} f (x) = - 2, \lim_{x \to 0^{-}} f (x) = 3$ and $f (0) = - 2$ .

Step 2. Find limx→0f(x).

Here left-hand limit and the right-hand limit are not equal.

$\begin{array}{rcl} \lim_{x \to 0^{+}} f (x) & \neq & \lim_{x \to 0^{-}} f (x) \\ - 2 & \neq & 3 \end{array}$

So, the limit of $f (x)$ as $x$ approaches to $0$ does not exist.

Step 3. Simplified answer.

Hence, $\lim_{x \to 0} f (x)$ does not exist.

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If $\lim_{x \to 0^{+}} f (x) = - 2$ , $\lim_{x \to 0^{-}} f (x) = 3$ , and $f (0) = - 2$ , what can you say about $\lim_{x \to 0} f (x)$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find limx→0f(x).

Step 3. Simplified answer.

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If limx→0+f(x)=-2, limx→0-f(x)=3, and f(0)=-2, what can you say about limx→0f(x)?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find limx→0f(x).

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

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If $\lim_{x \to 0^{+}} f (x) = - 2$ , $\lim_{x \to 0^{-}} f (x) = 3$ , and $f (0) = - 2$ , what can you say about $\lim_{x \to 0} f (x)$ ?