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

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

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limit as x approaches infinity of (1+1/(2x))^{3x}

x \to \infty lim ((1 + \frac{1}{2 x})^{3 x})

e^{\frac{3}{2}}

Decimal Notation

4.48168 \dots

Solution steps

x \to \infty lim ((1 + \frac{1}{2 x})^{3 x})

Apply exponent rules

= x \to \infty lim (e^{3 x l n (1 + \frac{1}{2 x})})

Apply the Limit Chain Rule:

e^{\frac{3}{2}}

= e^{\frac{3}{2}}

\int_{2}^{6} t^{3} ln (4 t) d t

y^{^{'}} = 5 y sin (4 x), y (\frac{π}{8}) = 3

n = 1 \sum \infty \frac{1}{π ^{n}}

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

y^{^{''}} + 2 y^{^{'}} - 63 y = 0

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