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 left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 0 lim (sin (x) ln (\frac{1}{x}))

x \to 4 lim (\frac{x ^{2}}{21})

x \to \infty lim (5 x + 1)

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

x \to 1 + lim (ln (x - 1) + 3 x)

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