What is the limit of the moment of inertia of a material line as a approaches 0?

[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?
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]

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)

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.