What is the limit as x approaches 0 of (1+6x)^{5/x} ?

The limit as x approaches 0 of (1+6x)^{5/x} is e^{30}

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limit as x approaches 0 of (1+6x)^{5/x}

x \to 0 lim ((1 + 6 x)^{\frac{5}{x}})

e^{30}

Solution steps

x \to 0 lim ((1 + 6 x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

e^{30}

= e^{30}

\int x e^{x} d x

t \to 0 lim (- 1)

\frac{d x}{d t} - (tan (t)) x = sin (t), x (0) = 1

\frac{d}{d x} (x^{3} e^{- x^{2}})

\frac{d}{d x} ((5 x + 3)^{2})

What is the limit as x approaches 0 of (1+6x)^{5/x} ?
The limit as x approaches 0 of (1+6x)^{5/x} is e^{30}