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

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

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

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

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

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

Cancel the common factor:

x

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

For

x

approaching

- 1

from the right

, x > - 1 \Rightarrow x (- \frac{1}{x ^{2}} + 1) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

\int_{0}^{4} 5 e^{- x^{2}} d x

\frac{cot ( x )}{x}

x \to 0 lim (\frac{20 sin ( x )}{4})

x \to 0 lim (x (e^{x} - 1) ln (x))

\int sin (\frac{π x}{3}) d x

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