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

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

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

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

a

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= a

x \to 1 lim (\frac{1}{2})

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x \to \infty lim ([x])

x \to 1 lim (f (x) x)

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

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