Chapter 1: Q. 5 (page 135)

Explain why we can’t calculate every limit $\lim_{x \to c} f (x)$ just by evaluating f(x) at $x = c$ . Support your argument with the graph of a function f for which $\lim_{x \to c} f (x) = f (c)$ .

Short Answer

Expert verified

We cannot calculate every limit $\lim_{x \to c} f (x)$ just by evaluating f(x) at $x = c$ .

Step by step solution

Step 1. Given information.

We cannot calculate every limit $\lim_{x \to c} f (x)$ just by evaluating $f (x)$ at $x = c$ .

Step 2. Explanation.

For the limit expression $\lim_{x \to 1} \frac{x - 1}{x^{2} - 1}$ , we cannot put $x = 1$ in the limit expression to get the value.

$\lim_{x \to 1} \frac{x - 1}{x^{2} - 1} = \frac{1 - 1}{1^{2} - 1} = \frac{0}{1 - 1} = \frac{0}{0}$

So, $\frac{0}{0}$ is undefined.

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Explain why we can’t calculate every limit $\lim_{x \to c} f (x)$ just by evaluating f(x) at $x = c$ . Support your argument with the graph of a function f for which $\lim_{x \to c} f (x) = f (c)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

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Explain why we can’t calculate every limit limx→cf(x) just by evaluating f(x) at x=c. Support your argument with the graph of a function f for which limx→cf(x)=f(c).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

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Explain why we can’t calculate every limit $\lim_{x \to c} f (x)$ just by evaluating f(x) at $x = c$ . Support your argument with the graph of a function f for which $\lim_{x \to c} f (x) = f (c)$ .