Chapter 1: Q 5. (page 86)

If $\lim_{x \to 2^{+}} f (x) = 8$ but $\lim_{x \to 2} f (x)$ does not exist, what can you say about $\lim_{x \to 2^{-}} f (x)$ ?

Short Answer

Expert verified

The value of $\lim_{x \to 2^{-}} f (x)$ cannot be said as it is unknown.

Step by step solution

Step 1. Given information.

It is given that $\lim_{x \to 2^{+}} f (x) = 8$ and $\lim_{x \to 2} f (x)$ does not exist.

Step 2. Determine the value of limx→2-f(x).

The value of $\lim_{x \to 2^{+}} f (x)$ is equal to $8$ does not mean that $\lim_{x \to 2^{-}} f (x) = 8$ .

Also, it is given that $\lim_{x \to 2} f (x)$ does not exist.

So, the value of $\lim_{x \to 2^{-}} f (x)$ cannot be said as it is not given.

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If $\lim_{x \to 2^{+}} f (x) = 8$ but $\lim_{x \to 2} f (x)$ does not exist, what can you say about $\lim_{x \to 2^{-}} f (x)$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value of limx→2-f(x).

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If limx→2+f(x)=8but limx→2f(x)does not exist, what can you say aboutlimx→2-f(x)?

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Step by step solution

Step 1. Given information.

Step 2. Determine the value of limx→2-f(x).

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If $\lim_{x \to 2^{+}} f (x) = 8$ but $\lim_{x \to 2} f (x)$ does not exist, what can you say about $\lim_{x \to 2^{-}} f (x)$ ?