What is the limit as x approaches 7-of (5x)/(x-7) ?

The limit as x approaches 7-of (5x)/(x-7) is -infinity

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limit as x approaches 7-of (5x)/(x-7)

x \to 7 - lim (\frac{5 x}{x - 7})

- \infty

Solution steps

x \to 7 - lim (\frac{5 x}{x - 7})

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

= 5 \cdot x \to 7 - lim (\frac{x}{x - 7})

Divide by highest denominator power:

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

= 5 \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

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 1 lim (e^{\frac{1}{x}})

x \to 2 lim (2 x^{2} - 3 x + 4)

x \to \infty + lim ((- 1)^{x})

x \to 0 lim (\frac{4 - x}{2 + 7 x})

x \to 1 lim (x^{2} - 2 x - 3)

What is the limit as x approaches 7-of (5x)/(x-7) ?
The limit as x approaches 7-of (5x)/(x-7) is -infinity