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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Simplify

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

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

Plug in the value

x = 2

= \frac{1}{2}

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

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

\frac{d}{d x} (7 x^{5})

\frac{x - 3 x x}{x}

\frac{d}{d x} (\frac{cos ( x )}{- 2 sin ( 2 x )})

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