What is the limit as x approaches 7+of (6x)/(x-7) ?

The limit as x approaches 7+of (6x)/(x-7) is infinity

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limit as x approaches 7+of (6x)/(x-7)

x \to 7 + lim (\frac{6 x}{x - 7})

\infty

Solution steps

x \to 7 + lim (\frac{6 x}{x - 7})

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

= 6 \cdot x \to 7 + lim (\frac{x}{x - 7})

Divide by highest denominator power:

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

= 6 \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

= 6 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{\partial}{\partial y} (- y^{2})

(3.6) (- 5.2)

\int_{1}^{12} - x^{2} - 11 x + 12 d x

\frac{d}{d x} \frac{( 2 x ^{2} + 10 ) ^{\frac{3}{2}}}{x - 1}

- 3 x

What is the limit as x approaches 7+of (6x)/(x-7) ?
The limit as x approaches 7+of (6x)/(x-7) is infinity