What is the limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x ?

The limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x is -1/36

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limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x

x \to 0 lim \frac{( ( 6 + x ) ^{- 1} - 6 ^{- 1} )}{x}

- \frac{1}{36}

Decimal

- 0.02777 \dots

Solution steps

x \to 0 lim (\frac{( 6 + x ) ^{- 1} - 6 ^{- 1}}{x})

Simplify

\frac{( 6 + x ) ^{- 1} - 6 ^{- 1}}{x} : - \frac{1}{6 ( x + 6 )}

= x \to 0 lim (- \frac{1}{6 ( x + 6 )})

Plug in the value

x = 0

= - \frac{1}{6 ( 0 + 6 )}

Simplify

= - \frac{1}{36}

What is the limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x ?
The limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x is -1/36