What is the limit as x approaches 0 of (1+5x)^{4/x} ?

The limit as x approaches 0 of (1+5x)^{4/x} is e^{20}

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limit as x approaches 0 of (1+5x)^{4/x}

x \to 0 lim ((1 + 5 x)^{\frac{4}{x}})

e^{20}

Decimal Notation

485165195.40978 \dots

Solution steps

x \to 0 lim ((1 + 5 x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (1 + 5 x)})

Apply the Limit Chain Rule:

e^{20}

= e^{20}

\frac{d y}{d x} - \frac{y}{x} = 3 x e^{x}, y (1) = 3 e - 2

y = - \frac{5 t}{( t + 8 ) ^{2}}

\int (x)^{3} arccos (x) d x

\int \frac{1}{1 + sin ( 2 x )} d x

\frac{2}{1 + x}

What is the limit as x approaches 0 of (1+5x)^{4/x} ?
The limit as x approaches 0 of (1+5x)^{4/x} is e^{20}