Chapter 3: Q. 15 (page 310)

Calculate each of the limits in Exercises 15–20 (a) using L’Hôpital’s rule and (b) without using L’Hôpital’s rule.
15. $\lim_{x \to 1} \frac{x^{2} + x - 2}{x - 1}$

Short Answer

Expert verified

The value of the limit is $3$

Step by step solution

Part (a) Step 1. Given information

We have been given the limit as $\lim_{x \to 1} \frac{x^{2} + x - 2}{x - 1}$

Part (a) Step 2. Find the limit using L’Hôpital’s rule.

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

Part (b) Step 1. Find the limit without using L’Hôpital’s rule.

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

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Calculate each of the limits in Exercises 15–20 (a) using L’Hôpital’s rule and (b) without using L’Hôpital’s rule.
15. $\lim_{x \to 1} \frac{x^{2} + x - 2}{x - 1}$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Find the limit using L’Hôpital’s rule.

Part (b) Step 1. Find the limit without using L’Hôpital’s rule.

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Calculate each of the limits in Exercises 15–20 (a) using L’Hôpital’s rule and (b) without using L’Hôpital’s rule.15.limx→1x2+x-2x-1

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Find the limit using L’Hôpital’s rule.

Part (b) Step 1. Find the limit without using L’Hôpital’s rule.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises 15–20 (a) using L’Hôpital’s rule and (b) without using L’Hôpital’s rule.
15. $\lim_{x \to 1} \frac{x^{2} + x - 2}{x - 1}$