What is the limit as x approaches 0+of (1+2x)^{3/x} ?

The limit as x approaches 0+of (1+2x)^{3/x} is e^6

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limit as x approaches 0+of (1+2x)^{3/x}

x \to 0 + lim ((1 + 2 x)^{\frac{3}{x}})

e^{6}

Decimal Notation

403.42879 \dots

Solution steps

x \to 0 + lim ((1 + 2 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + 2 x)})

Apply the Limit Chain Rule:

e^{6}

= e^{6}

(2 x - 7)^{5}

y^{^{''}} + 4 y = 2 x e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

y = 8 x^{2} - 6

f (x) = \frac{2}{4} x^{5} - \frac{1}{3} x^{3} + \frac{3}{6} x^{2} + \frac{1}{2} x

\frac{d}{d x} (arcsin (x^{6}))

What is the limit as x approaches 0+of (1+2x)^{3/x} ?
The limit as x approaches 0+of (1+2x)^{3/x} is e^6