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}

f (x) = e^{x^{5} + 2 x}

y = x^{2} y^{3} + x^{3} y^{2}

\frac{d y}{d x} = e^{(6 x - 3 y)}

\frac{d}{d x} (\frac{1}{( 16 - x ^{2} )})

\int 10 1 + cos (4 x) d x

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