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

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

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

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

ln (x)

Solution steps

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

Apply L'Hopital's Rule

: y \to 0 lim (\frac{x ^{y} ln ( x )}{1})

= y \to 0 lim (\frac{x ^{y} ln ( x )}{1})

Plug in the value

y = 0

= \frac{x ^{0} ln ( x )}{1}

Simplify

= ln (x)

8 8 x^{2} + 5

x \to 0 - lim (\frac{4}{sin ( x )})

\int x e^{- a x^{2}} d x

y^{^{'}} = 4 e^{x + y}

4 x^{2} - 5 x

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