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 right

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

The denominator is a positive quantity approaching 0 from the right

= 9 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{d}{d x} (e^{x} - x^{2})

\int \frac{1}{x + x ln ^{2} ( x )} d x

\int (9 t^{2} + \frac{1}{t ^{3}}) d t

\frac{d ^{2}}{d x ^{2}} (- sin (3 x))

\int x + 6 - x^{2} d x

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