What is the limit as x approaches 9-of (5x)/(x-9) ?

The limit as x approaches 9-of (5x)/(x-9) is -infinity

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limit as x approaches 9-of (5x)/(x-9)

x \to 9 - lim (\frac{5 x}{x - 9})

- \infty

Solution steps

x \to 9 - lim (\frac{5 x}{x - 9})

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

= 5 \cdot x \to 9 - lim (\frac{x}{x - 9})

Divide by highest denominator power:

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

= 5 \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

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (- 4 x^{4} + 8 x^{3})

\frac{( 3 s + 1 )}{s ( s + 2 )}

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{5} )}{x ^{18}}, y (1) = 1

g (x) = 3 (5 - 7 x)^{5}

\frac{d x}{d y} = 7 sin (x) + 3 cos (x)

What is the limit as x approaches 9-of (5x)/(x-9) ?
The limit as x approaches 9-of (5x)/(x-9) is -infinity