Limit of the form ∞-∞

[Victim]

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.

 

[Ray Vickson]

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 $\sqrt{A} - \sqrt{B}$.

 

[Victim]

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.