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

The limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x is -1/16

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limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x

x \to 0 lim (\frac{( 4 + x ) ^{- 1} - 4 ^{- 1}}{x})

- \frac{1}{16}

Decimal

- 0.0625

Solution steps

x \to 0 lim (\frac{( 4 + x ) ^{- 1} - 4 ^{- 1}}{x})

Simplify

\frac{( 4 + x ) ^{- 1} - 4 ^{- 1}}{x} : - \frac{1}{4 ( x + 4 )}

= x \to 0 lim (- \frac{1}{4 ( x + 4 )})

Plug in the value

x = 0

= - \frac{1}{4 ( 0 + 4 )}

Simplify

= - \frac{1}{16}

What is the limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x ?
The limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x is -1/16