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

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

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

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

e^{20}

Decimal Notation

485165195.40978 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{20}

= e^{20}

\frac{d y}{d x}, y^{5} = x^{7}

x^{2} + 3 x + \frac{1}{x ^{2}}

\int \frac{arcsin ( 4 x )}{1 - 16 x ^{2}} d x

\frac{x ^{2}}{7 + x}

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