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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

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

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

For

x

approaching

1

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - \infty

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