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 left

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

The denominator is a negative quantity approaching 0 from the left

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 5 + lim (\frac{4}{x ^{2} - 25})

x \to 0 lim (\frac{( x - 1 )}{x ^{2}})

x \to - 3 lim (2 x + 8)

x \to \infty lim (e^{x} - e)

x \to \infty lim (- 15)

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