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

The limit as x approaches 0+of (1+ax)^{1/x} is e^a

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

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

e^{a}

Solution steps

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

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (1 + a x)})

Apply the Limit Chain Rule:

e^{a}

= e^{a}

\frac{\partial}{\partial x} (e^{y} (x^{2} - y^{2}))

\int - 3 sin (3 x) d x

\int 2 x cos (x) d x

(5 x)^{9 x}

\frac{d}{d x} ((ln (\frac{1}{x}))^{3})

What is the limit as x approaches 0+of (1+ax)^{1/x} ?
The limit as x approaches 0+of (1+ax)^{1/x} is e^a