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})

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

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

x \to 1 - lim (x + 2) = 3

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

= 3 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to + 0 lim ((tan (9 x))^{x})

x \to \infty lim (\frac{25}{x})

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

x \to 3 lim (\frac{x}{3 x - 1})

x \to - 5 lim (\frac{7}{x + 5})

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