Find the limit of x^2(√(x^4+5)-x^2) as x->∞

[NWeid1]

Find the limit of x^2(√(x^4+5)-x^2) as x->∞. I think it might be a L'Hospitals rule, but I'm not sure. We haven't done many problems like this yet, thanks!

 

[SteamKing]

L'Hospital's Rule is valid only for certain indeterminate forms, like infinity/infinity or 0/0.
You should be able to determine this limit by inspection.

 

[Mark44]

Find the limit of x^2(√(x^4+5)-x^2) as x->∞. I think it might be a L'Hospitals rule, but I'm not sure. We haven't done many problems like this yet, thanks!

L'Hospital's Rule is valid only for certain indeterminate forms, like infinity/infinity or 0/0.

Right. L'Hopital's Rule is not applicable here.

You should be able to determine this limit by inspection.

I don't know about that. This limit is another of the indeterminate forms - [∞ * 0].

I would multiply the expression in the limit by 1, in the form of $\sqrt{x^4 + 5} + x^2$ over itself.