Limits

Calculus Level 3

$\Large \lim_{x\to0} (1+5x)^{\frac3{5x}} = \, ?$

1

e^{5/3}

e^{-5}

e^{-3}

e^{-5/3}

e^3

e^{5}

2

1 solution

Daniel Like
Jun 16, 2016

The answer to this problem can be found by writing the equation $y=(1+5x)^{3/5x}$ and taking the natural log of each side, which results in $lny=$ $\frac{3ln(1+5x)}{5x}$ . Using l'Hopital's rule to find the limit of lny as x approaches 0, you can find that lny approaches 3. Therefore, y approaches $e^{3}$ .

Limits

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