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 left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 0 - lim (\frac{3 x ^{2} + 2 x}{x})

x \to 0 + lim ((1 + 3 x)^{\frac{2}{x}})

x \to 0 lim (\frac{x + 5}{x - 3})

b \to 0 lim (cot (b) - csc (b))

x \to 7 - lim (\frac{x ^{2} - 4 x - 21}{∣ x - 7 ∣})

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