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

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

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

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

- \infty

Solution steps

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

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

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

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

= 2 \cdot 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

= 2 \cdot 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

= 2 \cdot 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

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