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 Notation

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}

\frac{d}{d x} (4 e^{3 x} + 12 x e^{3 x})

sin (5 t)

\frac{\partial}{\partial x} (- 3 x y (- 3 - x - y))

\frac{d y}{d x} = \frac{( x ^{2} + y )}{x ^{3}}

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