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

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

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

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

e^{12}

Decimal Notation

162754.79141 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{12}

= e^{12}

x \to 0 lim (x + [x])

x \to 10 lim (20)

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

x \to 1 lim (x^{3} + 4 x - 20)

x \to 3 lim (25)

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