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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

(1, 0), (0, 1)

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