What is the limit as x approaches-7-of (-9x)/(x+7) ?

The limit as x approaches-7-of (-9x)/(x+7) is -infinity

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limit as x approaches-7-of (-9x)/(x+7)

x \to - 7 - lim (\frac{- 9 x}{x + 7})

- \infty

Solution steps

x \to - 7 - lim (\frac{- 9 x}{x + 7})

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

= - 9 \cdot x \to - 7 - lim (\frac{x}{x + 7})

Divide by highest denominator power:

\frac{1}{1 + \frac{7}{x}}

= - 9 \cdot x \to - 7 - lim (\frac{1}{1 + \frac{7}{x}})

For

x

approaching

- 7

from the left

, x < - 7 \Rightarrow 1 + \frac{7}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 9 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int \frac{x + 3}{x} d x

x \to 4 lim (25 - x^{2})

x \to 0 lim ((x + 1)^{2} - x^{2})

\frac{\partial}{\partial x} (x^{8} + x y^{5} + 5)

y = 2 (6 x^{9} - 10 x + 4)^{- 3}

What is the limit as x approaches-7-of (-9x)/(x+7) ?
The limit as x approaches-7-of (-9x)/(x+7) is -infinity