Limit of the form ∞-∞

  • #1
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Homework Statement

lim x~∞ 〈√(x⁴+ax³+3x²+ bx+ 2) - √(x⁴+ 2x³- cx²+ 3x- d) 〉=4 then find a, b, c and d[/B]


Homework Equations


all the methods to find limits

The Attempt at a Solution


it can be said that the limit is of the form ∞-∞.I am completely stuck at this question.the answer is a=2 b∈ R c=5 d∈R.I think that this question can be solved by the concept of dominating terms.
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement

lim x~∞ 〈√(x⁴+ax³+3x²+ bx+ 2) - √(x⁴+ 2x³- cx²+ 3x- d) 〉=4 then find a, b, c and d[/B]


Homework Equations


all the methods to find limits

The Attempt at a Solution


it can be said that the limit is of the form ∞-∞.I am completely stuck at this question.the answer is a=2 b∈ R c=5 d∈R.I think that this question can be solved by the concept of dominating terms.
You were already given all the hints you need in your other similar post. Remember your elementary algebra: ##u^2 - v^2 = (u-v)(u+v)##, so for positive ##A## and ##B## we can write
$$A-B = (\sqrt{A} - \sqrt{B}) (\sqrt{A} + \sqrt{B}).$$
You can use this to re-write ##\sqrt{A} - \sqrt{B}##.
 
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Likes Victim
  • #3
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You were already given all the hints you need in your other similar post. Remember your elementary algebra: ##u^2 - v^2 = (u-v)(u+v)##, so for positive ##A## and ##B## we can write
$$A-B = (\sqrt{A} - \sqrt{B}) (\sqrt{A} + \sqrt{B}).$$
You can use this to re-write ##\sqrt{A} - \sqrt{B}##.
THANKS I got it.
 

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