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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

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

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

For

x

approaching

2

from the left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

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