What is the limit as x approaches 0+of (1+4x)^{3/x} ?

The limit as x approaches 0+of (1+4x)^{3/x} is e^{12}

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limit as x approaches 0+of (1+4x)^{3/x}

x \to 0 + lim ((1 + 4 x)^{\frac{3}{x}})

e^{12}

Decimal

162754.79141 \dots

Solution steps

x \to 0 + lim ((1 + 4 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + 4 x)})

Apply the Limit Chain Rule:

e^{12}

= e^{12}

\int_{0}^{5} - x^{2} + 5 x d x

\frac{d y}{d x} = y + x

\int_{0}^{2} t^{3} d t

\int x \cdot e^{3 \cdot x} d x

x \to - 3 lim (5 (3 x^{2} - 24 x + 3))

What is the limit as x approaches 0+of (1+4x)^{3/x} ?
The limit as x approaches 0+of (1+4x)^{3/x} is e^{12}