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

NWeid1 · Nov 15, 2011

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 · Nov 15, 2011

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 · Nov 15, 2011

NWeid1 said: ↑

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 said: ↑

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.

SteamKing said: ↑

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 [itex]\sqrt{x^4 + 5} + x^2[/itex] over itself.

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

NWeid1

SteamKing

Mark44

Staff: Mentor