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

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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 negative quantity approaching 0 from the left

= - \infty

x \to 1 lim (3 x - 3)

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

x \to - 1 lim (4 x + 5)

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

x \to - 4 lim (\frac{x + 4}{x + 4})

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