What is the limit as x approaches 2-of (5x)/(x-2) ?

The limit as x approaches 2-of (5x)/(x-2) is -infinity

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limit as x approaches 2-of (5x)/(x-2)

x \to 2 - lim (\frac{5 x}{x - 2})

- \infty

Solution steps

x \to 2 - lim (\frac{5 x}{x - 2})

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

= 5 \cdot x \to 2 - lim (\frac{x}{x - 2})

Divide by highest denominator power:

\frac{1}{1 - \frac{2}{x}}

= 5 \cdot x \to 2 - lim (\frac{1}{1 - \frac{2}{x}})

For

x

approaching

2

from the left

, x < 2 \Rightarrow 1 - \frac{2}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

(x + i y)^{2}

y^{^{'}} + (\frac{2}{x}) y = 0

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

f (x) = 5 + 5 x^{2} - 2 x^{3}, at x = 2

\frac{\partial}{\partial x} (\frac{G ( m , x ) m}{x ^{2}})

What is the limit as x approaches 2-of (5x)/(x-2) ?
The limit as x approaches 2-of (5x)/(x-2) is -infinity