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Chapter 2: Q. 2TF (page 223)

Show that each of the following limits is of the form $\frac{0}{0}$ and then use L’Hopital’s rule to calculate the limit: ˆ

Short Answer

Expert verified

The solution is 1

Step by step solution

Step 1. Given Information

Given limit is $\lim_{x \to 1} \frac{\ln (x)}{x - 1}$

Step 2. Calculate the limit

$\lim_{x \to 1} \frac{\ln (x)}{x - 1} \lim_{x \to 1} \frac{\frac{d (\ln (x))}{d x}}{\frac{d (x - 1)}{d x}} = \lim_{x \to 1} \frac{\frac{1}{x}}{1} = \lim_{x \to 1} \frac{1}{x} = 1$

Step 3. The solution

The solution is 1

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Show that each of the following limits is of the form 00and then use L’Hopital’s rule to calculate the limit: ˆ

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculate the limit

Step 3. The solution

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Show that each of the following limits is of the form $\frac{0}{0}$ and then use L’Hopital’s rule to calculate the limit: ˆ