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{\partial}{\partial x} (e^{3 x^{2} + y} (x - y))

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

\int (x^{2} (x^{3} - 1)^{10}) d x

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

\int \frac{3 x ^{2} + 5 x + 3}{( x ^{2} + 1 ) ^{2}} d x

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}