What is the limit as x approaches 1+of (x^2)/(x^2-1) ?

The limit as x approaches 1+of (x^2)/(x^2-1) is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 1+of (x^2)/(x^2-1)

x \to 1 + lim (\frac{x ^{2}}{x ^{2} - 1})

\infty

Solution steps

x \to 1 + lim (\frac{x ^{2}}{x ^{2} - 1})

Divide by highest denominator power:

\frac{1}{1 - \frac{1}{x ^{2}}}

= x \to 1 + lim (\frac{1}{1 - \frac{1}{x ^{2}}})

For

x

approaching

1

from the right

, x > 1 \Rightarrow 1 - \frac{1}{x ^{2}} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

What is the limit as x approaches 1+of (x^2)/(x^2-1) ?
The limit as x approaches 1+of (x^2)/(x^2-1) is infinity