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

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

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limit as x approaches 0 of (e^x+x)^{m/x}

x \to 0 lim ((e^{x} + x)^{\frac{m}{x}})

e^{2 m}

Solution steps

x \to 0 lim ((e^{x} + x)^{\frac{m}{x}})

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2 m}

= e^{2 m}

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