What is the limit as x approaches-5-of |(-2x)/(x+5)| ?

The limit as x approaches-5-of |(-2x)/(x+5)| is infinity

Popular >

limit as x approaches-5-of |(-2x)/(x+5)|

x \to - 5 - lim (\frac{- 2 x}{x + 5})

\infty

Solution steps

x \to - 5 - lim (\frac{- 2 x}{x + 5})

\frac{- 2 x}{x + 5}

is negative when

x \to - 5 -

. Therefore

\frac{- 2 x}{x + 5} = \frac{2 x}{x + 5}

= x \to - 5 - lim (\frac{2 x}{x + 5})

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

= 2 \cdot x \to - 5 - lim (\frac{x}{x + 5})

Divide by highest denominator power:

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

= 2 \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

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 lim (\frac{1}{x} - \frac{1}{x ^{3} - x})

x \to 1 lim (\frac{1}{1 - x ^{3}})

x \to 4 lim (x^{2} + 3 x - 5)

x \to 2 lim ((x - 1)^{\frac{6}{( x - 2 )}})

y \to 0 lim (\frac{- 1}{∣ y ∣})

What is the limit as x approaches-5-of |(-2x)/(x+5)| ?
The limit as x approaches-5-of |(-2x)/(x+5)| is infinity