Chapter 1: Q. 21 (page 153)

Consider the limit expression
$\lim_{x \to \infty} \frac{\sqrt{x}}{1 - \sqrt{x}}$
Calculate the limit.

Short Answer

Expert verified

The limit of the expression is $\infty .$

Step by step solution

Step 1. Given

The given expression is $\lim_{x \to \infty} \frac{\sqrt{x}}{1 - \sqrt{x}}$ .

Step 2. Calculation

The evaluated expression is

$\lim_{x \to \infty} \frac{\sqrt{x}}{1 - \sqrt{x}} = \frac{\lim_{x \to \infty} \sqrt{x}}{\lim_{x \to \infty} (1 - \sqrt{x})} = \frac{\lim_{x \to \infty} \sqrt{x}}{\lim_{x \to \infty} 1 - \lim_{x \to \infty} \sqrt{x}} = \frac{\sqrt{\infty}}{1 - \sqrt{\infty}} = \frac{\infty}{\infty} = \infty$

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.

Consider the limit expression
$\lim_{x \to \infty} \frac{\sqrt{x}}{1 - \sqrt{x}}$
Calculate the limit.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Statistics

Applied Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Consider the limit expressionlimx→∞x1-xCalculate the limit.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Statistics

Applied Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Consider the limit expression
$\lim_{x \to \infty} \frac{\sqrt{x}}{1 - \sqrt{x}}$
Calculate the limit.