What is the limit as x approaches 0 of ((2-x)^{-1}-2^{-1})/x ?

The limit as x approaches 0 of ((2-x)^{-1}-2^{-1})/x is 1/4

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limit as x approaches 0 of ((2-x)^{-1}-2^{-1})/x

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Simplify

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

= x \to 0 lim (\frac{1}{2 ( - x + 2 )})

Plug in the value

x = 0

= \frac{1}{2 ( - 0 + 2 )}

Simplify

= \frac{1}{4}

x \to 0 lim (\frac{1 - cos ( 2 x )}{x sin ( 2 x )})

x \to 0 lim (\frac{1}{x} + \frac{1}{e ^{x} - 1})

x \to 4 lim (2 + 4 x)

x \to 3 lim (\frac{2 x + 1}{x - 1})

x \to \frac{π}{6} lim (2 sin (x))

What is the limit as x approaches 0 of ((2-x)^{-1}-2^{-1})/x ?
The limit as x approaches 0 of ((2-x)^{-1}-2^{-1})/x is 1/4