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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 + \frac{4}{x}}

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

For

x

approaching

- 4

from the right

, x > - 4 \Rightarrow 1 + \frac{4}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - 4 (- \infty)

Apply Infinity Property:

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

= \infty

f (x) = 2 sin^{2} (x)

\frac{\partial}{\partial x} (7 y e^{x})

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 7

\frac{d}{d x} (\frac{( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{x ^{2}})

12 x^{2} - 12 x - 2

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