Chapter 2: Q. 3TF (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
$\lim_{x \to 1} \frac{3^{x} - 3}{1 - x^{2}}$

Short Answer

Expert verified

The solution is $\frac{3 \log (3)}{- 2}$

Step by step solution

Step 1. Given information

The given limit is $\lim_{x \to 1} \frac{3^{x} - 3}{1 - x^{2}}$

Step2. Calculate limit

$\lim_{x \to 1} \frac{3^{x} - 3}{1 - x^{2}} \lim_{x \to 1} \frac{\frac{d (3^{x} - 3)}{d x}}{\frac{d (1 - x^{2})}{d x}} = \lim_{x \to 1} \frac{3^{x} \log (3)}{- 2 x} = \frac{3 \log (3)}{- 2}$

Step 3. The solution

The solution is $\frac{3 \log (3)}{- 2}$

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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
$\lim_{x \to 1} \frac{3^{x} - 3}{1 - x^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step2. Calculate limit

Step 3. The solution

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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: ˆlimx→13x-31-x2

Short Answer

Step by step solution

Step 1. Given information

Step2. Calculate limit

Step 3. The solution

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Most popular questions from this chapter

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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
$\lim_{x \to 1} \frac{3^{x} - 3}{1 - x^{2}}$