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

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

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limit as x approaches 0 of (1+x)^{3/x}

x \to 0 lim ((1 + x)^{\frac{3}{x}})

e^{3}

Decimal Notation

20.08553 \dots

Solution steps

x \to 0 lim ((1 + x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

y^{^{''}} - \frac{5}{t} y^{^{'}} + \frac{18}{t ^{2}} y = 0

\int (2 cot^{2} (x) - 3 tan^{2} (x)) d x

\frac{d}{d y} (x e^{y})

\int x^{2} e^{y} d y

\int \frac{1}{x ^{2} 144 - x ^{2}} d x

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