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

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

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

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

e^{3}

Decimal

20.08553 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{3}

= e^{3}

\int csc^{2} (3 x) cos (3 x) d x

x \to 0 lim (x - 2)

y^{^{''}} - 6 y^{^{'}} - 2 y + 1 = cos (2 x)

(x^{2} + 4) \frac{d y}{d x} + 3 x y = x

\int (x - 1)^{4} d x

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