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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

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

= 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

= - \infty

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x \to 0 lim (2 x - x ln (x))

\frac{d}{d x} (3 x^{2} + 2 x + 5)

x \to 0 lim ((7 x)^{3 x})

\int - cos (x) + sin (x) + 3 d x

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