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

The limit as x approaches+0 of (e^x+2x)^{1/(2x)} is e^{3/2}

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

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

e^{\frac{3}{2}}

Decimal Notation

4.48168 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{\frac{3}{2}}

= e^{\frac{3}{2}}

f (x) = x ln (x) - x

\int x x^{2} + 2 x + 4 d x

\frac{\partial}{\partial x} (x^{3} sin (5 y))

2 e^{- t} sin (2 t)

(1 + t e^{- t})^{3}

What is the limit as x approaches+0 of (e^x+2x)^{1/(2x)} ?
The limit as x approaches+0 of (e^x+2x)^{1/(2x)} is e^{3/2}