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

The limit as x approaches 0 of (1+ax)^{a/x} is e^{a^2}

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

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

e^{a^{2}}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{a^{2}}

= e^{a^{2}}

x = 3 - 3 y^{2}, x = 3 y^{2} - 3

\int \frac{2 x}{( x - 5 ) ^{2}} d x

\frac{d}{d x} (ln (4 + 5 x))

\frac{d}{d x} (a x^{n} + cy (x)^{n})

\frac{x}{3 1 + x ^{2}}

What is the limit as x approaches 0 of (1+ax)^{a/x} ?
The limit as x approaches 0 of (1+ax)^{a/x} is e^{a^2}