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})

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

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

x \to 1 - lim (x) = 1

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

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{d}{d x} ((x + 2)^{- 2})

f (x) = \frac{x}{e ^{x}}

y = 8 x - x^{2} (1.7)

\int_{0}^{2} 2 π x (4 - x^{2}) d x

\frac{1}{2} (6 t^{2} + t)^{- 3}

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