What is the limit as x approaches 2 of (2/x-1)/(x-2) ?

The limit as x approaches 2 of (2/x-1)/(x-2) is -1/2

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limit as x approaches 2 of (2/x-1)/(x-2)

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

- \frac{1}{2}

Solution steps

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

Simplify

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

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

Plug in the value

x = 2

= - \frac{1}{2}

x \to π lim (\frac{sin ( x )}{x})

\frac{d}{d x} (1 - sin (x))

f

t \cdot e^{- 2 t}

\int \frac{x ^{2} + 3 x - 2}{x ^{2}} d x

What is the limit as x approaches 2 of (2/x-1)/(x-2) ?
The limit as x approaches 2 of (2/x-1)/(x-2) is -1/2