What is the limit as x approaches 3+of (x^2)/(9-x^2) ?

The limit as x approaches 3+of (x^2)/(9-x^2) 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 3+of (x^2)/(9-x^2)

x \to 3 + lim (\frac{x ^{2}}{9 - x ^{2}})

- \infty

Solution steps

x \to 3 + lim (\frac{x ^{2}}{9 - x ^{2}})

Divide by highest denominator power:

\frac{1}{\frac{9}{x ^{2}} - 1}

= x \to 3 + lim (\frac{1}{\frac{9}{x ^{2}} - 1})

For

x

approaching

3

from the right

, x > 3 \Rightarrow \frac{9}{x ^{2}} - 1 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

What is the limit as x approaches 3+of (x^2)/(9-x^2) ?
The limit as x approaches 3+of (x^2)/(9-x^2) is -infinity