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

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

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

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

e^{ba}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{ba}

= e^{ba}

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