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 left

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

The denominator is a negative quantity approaching 0 from the left

= 6 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (- 1.2 x^{2} + 9.6 x)

\frac{( 1 - e ^{- 5 s} )}{s ^{2}}

\int \frac{1}{x ln ( x ) ln ^{2} ( x ) - 4} d x

\int (\frac{x ^{2}}{( 7 + x ^{3} ) ^{2}}) d x

\frac{\partial}{\partial x} (\frac{x \cdot y}{x - y})

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