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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

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

= - 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

= - (- \infty)

Simplify

= \infty

x \to - 6 lim (\frac{∣ x ∣}{x})

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

x \to 0 lim ((\frac{1 + 5 x}{1 + 2 x})^{\frac{1}{x}})

x \to 0 lim (\frac{( 1 + sin ( 2 x ) ) ^{\frac{1}{x}}}{x})

z \to 2 lim ((\frac{2 z - z ^{2}}{z ^{2} - 4})^{3})

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