Chapter 2: Q. 4TF (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
$\lim_{x \to 1} \frac{{(x - 3)}^{2}}{1 - e^{x - 3}}$

Short Answer

Expert verified

The solution is -2

Step by step solution

Step 1. Given information

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

Step 2. Calculate limit

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

Step 3. The solution

The solution is -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
$\lim_{x \to 1} \frac{{(x - 3)}^{2}}{1 - e^{x - 3}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. 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→1x-321-ex-3

Short Answer

Step by step solution

Step 1. Given information

Step 2. 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
$\lim_{x \to 1} \frac{{(x - 3)}^{2}}{1 - e^{x - 3}}$