What is the limit as x approaches 8+of (6x)/(x-8) ?

The limit as x approaches 8+of (6x)/(x-8) is infinity

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limit as x approaches 8+of (6x)/(x-8)

x \to 8 + lim (\frac{6 x}{x - 8})

\infty

Solution steps

x \to 8 + lim (\frac{6 x}{x - 8})

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

= 6 \cdot x \to 8 + lim (\frac{x}{x - 8})

Divide by highest denominator power:

\frac{1}{1 - \frac{8}{x}}

= 6 \cdot x \to 8 + lim (\frac{1}{1 - \frac{8}{x}})

For

x

approaching

8

from the right

, x > 8 \Rightarrow 1 - \frac{8}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 6 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{d}{d x} (3 x^{5 x})

\int x e^{7 x} d x

x^{2} + y^{2} = 25, y = 0

\int_{0}^{2} 3^{x} d x

arctan (2 x)

What is the limit as x approaches 8+of (6x)/(x-8) ?
The limit as x approaches 8+of (6x)/(x-8) is infinity