What is the limit as x approaches 9-of (6x)/(x-9) ?

The limit as x approaches 9-of (6x)/(x-9) is -infinity

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limit as x approaches 9-of (6x)/(x-9)

x \to 9 - lim (\frac{6 x}{x - 9})

- \infty

Solution steps

x \to 9 - lim (\frac{6 x}{x - 9})

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

= 6 \cdot x \to 9 - lim (\frac{x}{x - 9})

Divide by highest denominator power:

\frac{1}{1 - \frac{9}{x}}

= 6 \cdot x \to 9 - lim (\frac{1}{1 - \frac{9}{x}})

For

x

approaching

9

from the left

, x < 9 \Rightarrow 1 - \frac{9}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= 6 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (\frac{e ^{4 x}}{x})

\frac{d}{d t} (e^{a t})

\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

y^{^{''}} - y = 1

\frac{d y}{d x} = \frac{8 y ^{2}}{x}

What is the limit as x approaches 9-of (6x)/(x-9) ?
The limit as x approaches 9-of (6x)/(x-9) is -infinity