Results 1 to 6 of 6

Math Help - [SOLVED] Find values of a, b and c such that limit ... is finite?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    [SOLVED] Find values of a, b and c such that limit ... is finite?

    Find values of a, b and c such that:
    lim (cos 4x + a cos 2x + b)/x^4 = Finite
    x --> 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by fardeen_gen View Post
    Find values of a, b and c such that:
    lim (cos 4x + a cos 2x + b)/x^4 = Finite
    x --> 0
    You have missed a 'c' somewhere, thats why we will not be getting any answer correctly. But I will tell you the general idea...

    Let L be the limit.

    Observe that if g(0) = 0 and \lim_{x \to 0} \frac{f(x)}{g(x)} = L, then  \lim_{x \to 0} f(x) = 0 .

    Applying it here, we get 1 + a + b = 0.

    Now apply L'Hospital's rule, to get another form for L. Do the same process again.

    Alternate trick is to substitute the power series for cos and choosing coefficients such that the limit exists.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    No missing 'c' according to text.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by fardeen_gen View Post
    Find values of a, b and c such that:
    lim (cos 4x + a cos 2x + b)/x^4 = Finite
    x --> 0
    Quote Originally Posted by fardeen_gen View Post
    No missing 'c' according to text.
    Then why does the question say find a, b and c?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    You can however use power series or L'Hospitals to get the following equations:

    a+b+1 = 0 and 8 + 2a = 0 and thus a = -4 and b = 3. So the limit L = 8.

    To do this using power series, write \cos t = 1 - \frac{t^2}{2!} + \frac{t^4}{4!} + (t^6 ke terms ....). Then group terms with same powers in the numerator. All terms with constant and power of x^2 must go to 0. That will give you the above two equations....
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    The question was a general one, under which the specific problem appears(there are some which involve a, b and c, a and b, b and c... and so on).

    Thanks for the help!!
    I got the same answer right now!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 31st 2010, 09:19 PM
  2. Replies: 0
    Last Post: February 23rd 2010, 09:40 AM
  3. Replies: 2
    Last Post: January 28th 2010, 01:39 AM
  4. Find set of values of x for which limit = 0?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 10th 2009, 12:49 AM
  5. [SOLVED] Find the values of p and q
    Posted in the Algebra Forum
    Replies: 12
    Last Post: April 27th 2008, 02:33 AM

Search Tags


/mathhelpforum @mathhelpforum