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 Notation

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}

x \to 3 lim (x^{3} + 5 x - 1)

x \to 0 lim ((e^{x} + x)^{\frac{7}{x}})

x \to 3 lim (\frac{x ^{2} - 6 x - 9}{x - 3})

x \to - 8 lim (\frac{1}{x + 8})

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

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}