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Need Help, Stuck on Calc 1 Homework

  1. Feb 25, 2010 #1
    Need Help, Stuck on Calc 1 Homework!!

    1. Find constants A, B, and C such that the function [tex] y = Ax^2 + Bx + C [/tex] satisfies the equation [tex] y'' + y' - 2y = x^2 [/tex]


    2. Find [tex] \lim_{x \rightarrow 0} \frac{sin(a + 2x)-2sin(a + x)+sin a}{x^2}
    [/tex]


    3. If [tex] y = \frac{x}{\sqrt{a^2-1}} - \frac{2}{\sqrt{a^2-1}} \arctan\frac{\sin(x)}{a+\sqrt(a^2-1)+\cos(x)}
    [/tex] show that [tex] \frac{dy}{dx} = \frac{1}{a+\cos(x)} [/tex]



    I'm completely stuck with these questions; they are much harder than the ones on the exam. I'd appreciate anyone who can point me in the right direction as to where/how to start.
     
    Last edited: Feb 25, 2010
  2. jcsd
  3. Feb 25, 2010 #2

    LCKurtz

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    Re: Need Help, Stuck on Calc 1 Homework!!

    Hello King Kong, welcome to the Forums. You are pretty much required to show your attempt before you will receive much help. Since this is your first post, I will just give you a hint on the first one. Take the derivatives, plug them in, and see what A,B, and C work.
     
  4. Feb 25, 2010 #3
    Re: Need Help, Stuck on Calc 1 Homework!!

    Thanks for the welcome. I have attempted these problems on my own but got stuck and don't know how to continue.
    For problem #1, I took the first and second derivatives of [tex] y = Ax^2+Bx+C [/tex]
    [tex] y' = 2Ax + B [/tex] and [tex] y'' = 2A [/tex]. Then I plug them in and got:
    [tex] 2A + 2Ax + B - 2Ax^2 - 2BX - 2C = X^2 [/tex]. This is where I got stuck, what should I do next?

    For problem #2, I used the addition formula for sin which is sin(x+y) = sinxcosy + cosxsiny. But the result did not help me get rid of the X^2 in the denominator.

    As for problem #3, the only way I can think of is to apply the quotient and product rule, which will result in a long and tedious operation.

    I appreciate any additional hint/advice.
     
  5. Feb 25, 2010 #4
    Re: Need Help, Stuck on Calc 1 Homework!!

    For 1, on the left side of the equation there is only one term that has [tex]x^2[/tex], that is of course [tex]-2Ax^2[/tex], so from that you know that A must be -1/2, using that A you can figure out how all the other terms cancel out.
     
  6. Feb 25, 2010 #5
    Re: Need Help, Stuck on Calc 1 Homework!!

    I got A = -1/2 part and If I substitute -1/2 for A in the equation I get -1-x-B-2BX-2C = 0 but how do I use it to solve for other terms? Can you elaborate on that please? thanks!
     
  7. Feb 25, 2010 #6

    LCKurtz

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    Re: Need Help, Stuck on Calc 1 Homework!!

    You want it to come out x2 + 0x + 0.
     
  8. Feb 26, 2010 #7
    Re: Need Help, Stuck on Calc 1 Homework!!

    Bump... still need help with problem 2 and 3.
     
  9. Feb 26, 2010 #8
    Re: Need Help, Stuck on Calc 1 Homework!!

    For number 2, do you know Hopital's rule?
     
  10. Feb 26, 2010 #9
    Re: Need Help, Stuck on Calc 1 Homework!!

    Nope.
     
  11. Feb 26, 2010 #10
    Re: Need Help, Stuck on Calc 1 Homework!!

    http://en.wikipedia.org/wiki/L'Hôpital's_rule

    Take your numerator as a function, perhaps calling it f(x). Then call your denominator g(x) = x2. What is f ''(x) and g ''(x)? Then find the limit of f ''(x) / g ''(x).
     
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