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}

\int p (p + 2)^{4} d p

x \to 7 + lim (\frac{x + 1}{x - 7})

s (t) = 4 e^{- 2 t} sin (2 π t)

\int \frac{3 x + 7}{3 x + 8} d x

y^{^{'}} = \frac{( 6 x ^{3} + y ^{3} )}{x 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