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

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

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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})

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 right

, 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

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