Find the limit
lim x-> infinity [1/x] / [1/3 x ^(-2/3)]
First, I do not understand how I get to the simplyfied term:
lim x-> infinity 3 / x^1/3
Second, I do not understand why the answer is zero.
Thanks
$\displaystyle \frac{\frac{1}{x}}{\frac{1}{3}x^{-\frac{2}{3}}}$
$\displaystyle \frac{\frac{1}{x}}{\frac{1}{3x^{\frac{2}{3}}}}$
remember how to divide fractions?
$\displaystyle \frac{1}{x} \cdot \frac{3x^{\frac{2}{3}}}{1} = \frac{3}{x^{\frac{1}{3}}}$
now ... what happens to the value $\displaystyle \frac{3}{x^{\frac{1}{3}}}$ as x gets very large?