Victim said: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.
THANKS I got it.Ray Vickson said: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}##.
In order to solve for a, b, c, and d for ∞-∞ form, you will need to use algebraic techniques such as factoring, simplifying, and solving equations. Start by identifying which term(s) in the expression have an infinite value and then work backwards to determine the values of a, b, c, and d.
The values of a, b, c, and d for ∞-∞ form help us to determine the behavior of a function as it approaches infinity. They also help us to evaluate limits and determine if they exist or not.
Yes, L'Hospital's Rule can be used to solve for a, b, c, and d for ∞-∞ form. This rule states that if you have a limit of the form ∞-∞, you can take the derivative of the numerator and denominator separately and then evaluate the limit again.
Yes, there are a few restrictions when solving for a, b, c, and d for ∞-∞ form. First, the limit must exist in order for the values of a, b, c, and d to be determined. Additionally, the function must be continuous at the point where the limit is being evaluated.
One helpful tip is to try factoring the expression to see if any terms can be cancelled out. Another tip is to simplify the expression as much as possible before evaluating the limit. Additionally, it can be helpful to graph the function to visualize the behavior as it approaches infinity.