Chapter 3: Q. 29 (page 311)

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.
$\lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1})$

Short Answer

Expert verified

The value of the limit is $\infty$

Step by step solution

Step 1. Given information

Given function $\lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1})$

Apply L-Hospital rule and solve

Calculating, we get

$\lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \lim_{x \to \infty} (\frac{x e^{x} + e^{x} - e^{x}}{x + 1}) \lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \lim_{x \to \infty} (\frac{x e^{x}}{x + 1}) \lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \lim_{x \to \infty} (\frac{x e^{x} + e^{x} \cdot 1}{1 + 0}) \lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \lim_{x \to \infty} (x e^{x} + e^{x}) \lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \lim_{x \to \infty} e^{x} (x + 1) \lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1}) = \infty$

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 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.
$\lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1})$

Short Answer

Step by step solution

Step 1. Given information

Apply L-Hospital rule and solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Mechanics Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.limx→∞ex-exx+1

Short Answer

Step by step solution

Step 1. Given information

Apply L-Hospital rule and solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Mechanics Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.
$\lim_{x \to \infty} (e^{x} - \frac{e^{x}}{x + 1})$