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

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

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

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

\infty

Solution steps

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

Simplify

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

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

For

x

approaching

- 1

from the right

, x > - 1 \Rightarrow x + 1 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to - 3 lim (2 x - 1)

x \to - 5 lim (- 5 + 7 x - 8 x^{2} + x^{3})

x \to 8 + lim (3^{x - 6})

x \to 0 lim (ln (1 - 6 x))

x \to 100 lim (\frac{1}{x})

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