Chapter 3: Q. 16 (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.
16. $\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2}$

Short Answer

Expert verified

The value of the limit is $0$

Step by step solution

Part (a) Step 1. Given information

We have been given the limit as $\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2}$

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

$\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2} = \lim_{x \to 2} \frac{2 x - 4}{1} = 2 (2) - 4 = 0$

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

$\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2} = \lim_{x \to 2} \frac{{(x - 2)}^{2}}{x - 2} = \lim_{x \to 2} x - 2 = 2 - 2 = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Calculate each of the limits in Exercises 15–20 (a) using L’Hôpital’s rule and (b) without using L’Hôpital’s rule.
16. $\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2}$

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

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Logic and Functions

Calculus

Statistics

Probability and Statistics

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.16.limx→2x2-4x+4x-2

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

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Logic and Functions

Calculus

Statistics

Probability and Statistics

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.
16. $\lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x - 2}$