What is the limit of

1. Oct 4, 2005

thomate1

what is the limit of ......

I am a physics student. While I was doing problem concerned with moment of inertia, I got stuck at a point. I got the moment of inertia of a material line as

lim a -> 0 (3ab)/(a^3 + b^3)

What is the limit?

2. Oct 4, 2005

James R

The limit for the expression you've written is zero, provided b does not equal zero.

3. Oct 5, 2005

HallsofIvy

Staff Emeritus
And if b= 0, 3ab/(a^3+b^3)= 0 for all a so the limit is still 0!

4. Oct 6, 2005

thomate1

Sorry, question was wrong

I am sorry that the question I posed was not what I supposed. I meant

lim a->0 (a^3 + b^3)/(3ab)

5. Oct 6, 2005

ranger

It looks like the lim = 0, since a = 0.

Man its been a while since i did this stuff.

6. Oct 6, 2005

VietDao29

Nope. The limit does not exist here.
Since b is in the denominator, so $b \neq 0$
So
$$\lim_{a \rightarrow 0} \frac{a ^ 3 + b ^ 3}{3ab}$$
The numerator will tend to b3, while the denominator will tend to 0. So the limit does not exist.
Viet Dao,

7. Oct 6, 2005

ranger

Does that mean there is an asymptote there or something?

8. Oct 6, 2005

VietDao29

Yup, there's a vertical asymptote there.