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}

y^{^{''}} - 7 y^{^{'}} + 14 y = - 784 t^{2}

y^{^{''}} + 9 y = 3 tan (3 x)

\frac{x ^{2} - 6 x + 1}{x ^{2} + 9}

12 x^{11} y + x^{12} y^{^{'}} = - 7 sec^{2} (x) \cdot tan (x)

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