What is the limit as x approaches 7+of (9x)/(x-7) ?

The limit as x approaches 7+of (9x)/(x-7) is infinity

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limit as x approaches 7+of (9x)/(x-7)

x \to 7 + lim (\frac{9 x}{x - 7})

\infty

Solution steps

x \to 7 + lim (\frac{9 x}{x - 7})

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

= 9 \cdot x \to 7 + lim (\frac{x}{x - 7})

Divide by highest denominator power:

\frac{1}{1 - \frac{7}{x}}

= 9 \cdot x \to 7 + lim (\frac{1}{1 - \frac{7}{x}})

For

x

approaching

7

from the right

, x > 7 \Rightarrow 1 - \frac{7}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 9 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int 2 x + 3 e^{x} d x

x^{2} y^{^{''}} - x y^{^{'}} + y = ln (x)

f^{^{'}} (x) = 6 x, f (0) = 8

t y^{^{'}} + 2 y = 3 t^{2} - 3 t

\int t d t

What is the limit as x approaches 7+of (9x)/(x-7) ?
The limit as x approaches 7+of (9x)/(x-7) is infinity