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

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
Staff Emeritus
Homework Helper
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
Mentor
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.