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

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

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

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

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2}

= e^{2}

x \to 1.5 lim (\frac{1}{x - 2})

x y^{^{'}} + y = 4 x y^{2}, y (1) = 9

\int - 8 e^{x + 4} - \frac{5}{x + 7} - 5 sec^{2} (x + 6) d x

x \to - 1 + lim (x + 4)

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

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