What is the limit as x approaches 0 of ((9-x)^{-1}-9^{-1})/x ?

The limit as x approaches 0 of ((9-x)^{-1}-9^{-1})/x is 1/81

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limit as x approaches 0 of ((9-x)^{-1}-9^{-1})/x

x \to 0 lim (\frac{( 9 - x ) ^{- 1} - 9 ^{- 1}}{x})

\frac{1}{81}

Decimal

0.01234 \dots

Solution steps

x \to 0 lim (\frac{( 9 - x ) ^{- 1} - 9 ^{- 1}}{x})

Simplify

\frac{( 9 - x ) ^{- 1} - 9 ^{- 1}}{x} : \frac{1}{9 ( - x + 9 )}

= x \to 0 lim (\frac{1}{9 ( - x + 9 )})

Plug in the value

x = 0

= \frac{1}{9 ( - 0 + 9 )}

Simplify

= \frac{1}{81}

What is the limit as x approaches 0 of ((9-x)^{-1}-9^{-1})/x ?
The limit as x approaches 0 of ((9-x)^{-1}-9^{-1})/x is 1/81