What is the limit as x approaches 0+of (1+x)^{3/x} ?

The limit as x approaches 0+of (1+x)^{3/x} is e^3

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limit as x approaches 0+of (1+x)^{3/x}

x \to 0 + lim ((1 + x)^{\frac{3}{x}})

e^{3}

Decimal Notation

20.08553 \dots

Solution steps

x \to 0 + lim ((1 + x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

\frac{\partial}{\partial x} (e^{x} cos (x y))

\int_{1}^{6} f (\frac{1}{2} x) d x

\frac{d}{d x} (\frac{( 3 x ^{2} - 2 x - 3 )}{( x ^{2} + 1 ) ^{2}})

y^{^{'}} = x - x y

\int e^{s i n (t)} d t

What is the limit as x approaches 0+of (1+x)^{3/x} ?
The limit as x approaches 0+of (1+x)^{3/x} is e^3