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

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

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

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

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2}

= e^{2}

\frac{d}{d x} (x^{3} - 6 x^{2} - 10 x)

\frac{d}{d x} (5 cot (\frac{2}{x}))

\int 2^{c o s (x)} sin (x) d x

\int_{0}^{\frac{π}{4}} tan (x) d x

\frac{8}{3 s ^{2} + 12} + \frac{3}{s ^{2} - 49}

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