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

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The limit of x^2(√(x^4+5)-x^2) as x approaches infinity can be evaluated without L'Hospital's Rule, as it does not present an indeterminate form suitable for that method. Instead, multiplying the expression by a conjugate, (√(x^4 + 5) + x^2)/(√(x^4 + 5) + x^2), is suggested to simplify the limit. This approach transforms the expression into a more manageable form for analysis. The limit ultimately resolves to a specific value as x approaches infinity. Understanding the proper techniques for evaluating limits is crucial for tackling similar problems effectively.
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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!
 
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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.
 
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 \sqrt{x^4 + 5} + x^2 over itself.
 

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