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

The limit as x approaches 0 of ((1-x)^n-1)/x is -n

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limit as x approaches 0 of ((1-x)^n-1)/x

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

- n

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{- n ( - 0 + 1 ) ^{n - 1}}{1}

Simplify

= - n

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What is the limit as x approaches 0 of ((1-x)^n-1)/x ?
The limit as x approaches 0 of ((1-x)^n-1)/x is -n