What is the limit as x approaches-5-of (-4x)/(x+5) ?

The limit as x approaches-5-of (-4x)/(x+5) is -infinity

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limit as x approaches-5-of (-4x)/(x+5)

x \to - 5 - lim (\frac{- 4 x}{x + 5})

- \infty

Solution steps

x \to - 5 - lim (\frac{- 4 x}{x + 5})

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

= - 4 \cdot x \to - 5 - lim (\frac{x}{x + 5})

Divide by highest denominator power:

\frac{1}{1 + \frac{5}{x}}

= - 4 \cdot x \to - 5 - lim (\frac{1}{1 + \frac{5}{x}})

For

x

approaching

- 5

from the left

, x < - 5 \Rightarrow 1 + \frac{5}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 4 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int \frac{ln ( t ) t ^{- 1}}{- 3} d t

\frac{d}{d x} (ln (x^{2} + y^{3}))

\int x^{3} 4 - x^{2} d x

\int \frac{5 x ^{3} - 3 x ^{2} + 2}{2 x ^{2}} d x

\int_{0}^{3} 1 + x^{2} d x

What is the limit as x approaches-5-of (-4x)/(x+5) ?
The limit as x approaches-5-of (-4x)/(x+5) is -infinity