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}

\frac{\partial}{\partial x} ((y - x^{2}) (2 y^{2} + x))

\int \frac{5}{36 + x ^{2}} d x

\frac{\partial}{\partial y} (x y (1 - x - y))

y = x^{4} + 2 e^{x}

x \to 9 lim (∣ x + 3 ∣)

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}