1. ## limit at infinity

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

2. Originally Posted by DBA
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
$\frac{\frac{1}{x}}{\frac{1}{3}x^{-\frac{2}{3}}}$

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

remember how to divide fractions?

$\frac{1}{x} \cdot \frac{3x^{\frac{2}{3}}}{1} = \frac{3}{x^{\frac{1}{3}}}$

now ... what happens to the value $\frac{3}{x^{\frac{1}{3}}}$ as x gets very large?

3. Yes remember
3x^3/3-2/3 = 3x^1/3 Thanks, I got that now.

lim x->infinity 3/x^1/3 = 0

the nominator stays 3 and the denominator gets larger and larger. So, the entire term gets smaller and smaller. Thus closer and closer to zero.

Thanks!