# 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.