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 right

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

The denominator is a positive quantity approaching 0 from the right

= 5 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int (- 2 x) d x

\frac{d ^{4}}{d x ^{4}} (\frac{1}{1 + x})

f (x) = \frac{ln ( x ) - 1}{ln ^{2} ( x )}

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

y^{^{''}} - y^{^{'}} + y = 0

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