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

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

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limit as x approaches 0 of (1+x)^{2/x}

x \to 0 lim ((1 + x)^{\frac{2}{x}})

e^{2}

Decimal

7.38905 \dots

Solution steps

x \to 0 lim ((1 + x)^{\frac{2}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{2}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{2}

= e^{2}

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