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

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

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

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

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

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

For

x

approaching

- 5

from the right

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

The denominator is a negative quantity approaching 0 from the left

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

f (x) = 2 x^{2} - 9 x + 10

f^{^{'}} (x) = 6 x + 1 2^{\frac{3}{4}}

\int (e^{x} - e^{- x})^{2} d x

x \to 3 lim (x + 5)

\frac{\partial}{\partial y} (sin (8 x) cos (3 y))

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