What is the limit as x approaches 2-of (9x)/(x-2) ?

The limit as x approaches 2-of (9x)/(x-2) is -infinity

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limit as x approaches 2-of (9x)/(x-2)

x \to 2 - lim (\frac{9 x}{x - 2})

- \infty

Solution steps

x \to 2 - lim (\frac{9 x}{x - 2})

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

= 9 \cdot x \to 2 - lim (\frac{x}{x - 2})

Divide by highest denominator power:

\frac{1}{1 - \frac{2}{x}}

= 9 \cdot x \to 2 - lim (\frac{1}{1 - \frac{2}{x}})

For

x

approaching

2

from the left

, x < 2 \Rightarrow 1 - \frac{2}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= 9 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{\partial}{\partial y} (4 x + 9 y - 360)

\frac{( 2 x + 1 ) ( x ^{3} + 3 )}{x}

\int - 2 e^{2 x} d x

\int \frac{e ^{4 x}}{25 - e ^{2 x}} d x

\frac{\partial}{\partial x} (ln (x^{2} + 2 y^{2}))

What is the limit as x approaches 2-of (9x)/(x-2) ?
The limit as x approaches 2-of (9x)/(x-2) is -infinity