What is the limit as x approaches-7+of (-x^2)/(x+7) ?

The limit as x approaches-7+of (-x^2)/(x+7) is -infinity

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limit as x approaches-7+of (-x^2)/(x+7)

x \to - 7 + lim (\frac{- x ^{2}}{x + 7})

- \infty

Solution steps

x \to - 7 + lim (\frac{- x ^{2}}{x + 7})

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

= - x \to - 7 + lim (\frac{x ^{2}}{x + 7})

\frac{x ^{2}}{x + 7} = x^{2} \frac{1}{x + 7}

= - x \to - 7 + lim (x^{2} \frac{1}{x + 7})

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 - 7 + lim (x^{2}) \cdot x \to - 7 + lim (\frac{1}{x + 7})

x \to - 7 + lim (x^{2}) = 49

x \to - 7 + lim (\frac{1}{x + 7}) = \infty

= - 49 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches-7+of (-x^2)/(x+7) ?
The limit as x approaches-7+of (-x^2)/(x+7) is -infinity