What is the limit as x approaches 0 of (1+5x)^{3/x} ?

The limit as x approaches 0 of (1+5x)^{3/x} is e^{15}

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limit as x approaches 0 of (1+5x)^{3/x}

x \to 0 lim ((1 + 5 x)^{\frac{3}{x}})

e^{15}

Decimal

3269017.37247 \dots

Solution steps

x \to 0 lim ((1 + 5 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (1 + 5 x)})

Apply the Limit Chain Rule:

e^{15}

= e^{15}

d er i v a t i v e \frac{( x ^{4} + 2 )}{ln ( x )}

\frac{\partial}{\partial x} (e^{- x y})

n = 0 \sum \infty n^{2} x^{n}

\int (3 x + 2)^{4} d x

\frac{d}{d x} (e^{2 x} sin (6 x))

What is the limit as x approaches 0 of (1+5x)^{3/x} ?
The limit as x approaches 0 of (1+5x)^{3/x} is e^{15}