what is the limit of ......

[thomate1]

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?
Thanks in advance for your help

[James R]

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

[HallsofIvy]

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

[thomate1]

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


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

Thanks in advance for your help

[ranger]

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

Man its been a while since i did this stuff.

[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,

[ranger]

So the limit does not exist.

Does that mean there is an asymptote there or something?

[VietDao29]

Does that mean there is an asymptote there or something?
Yup, there's a vertical asymptote there.