What is the limit as x approaches+0 of (1+6x)^{4/x} ?

The limit as x approaches+0 of (1+6x)^{4/x} is e^{24}

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limit as x approaches+0 of (1+6x)^{4/x}

x \to + 0 lim ((1 + 6 x)^{\frac{4}{x}})

e^{24}

Decimal Notation

26489122129.843437

Solution steps

x \to 0 lim ((1 + 6 x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

e^{24}

= e^{24}

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

\int x e^{4 x^{2}} d x

x \to 5 + lim (\frac{x + 5}{x + 5})

\int x^{- 2} + x^{- 1} + 1 + x + cos (x) d x

n = 1 \sum \infty \frac{1}{2 \cdot n}

What is the limit as x approaches+0 of (1+6x)^{4/x} ?
The limit as x approaches+0 of (1+6x)^{4/x} is e^{24}