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Math Help - Finding sum of constants in limits

  1. #1
    Senior Member polymerase's Avatar
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    Finding sum of constants in limits

    If a,b,c,d are constants such that \displaystyle\lim_{x\to{0}}\frac{ax^2+sin\;bx+sin\  ;cx+sin\;dx}{2x^2+3x^3+4x^4} = 3 what is the value of the sum a+b+c+d?

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  2. #2
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    Use L'Hopital's rule.

    you get (0+b+c+d)/0

    I think the only way this limit can exist is if b+c+d = 0

    we then get the indeterminate form 0/0

    Use L'Hopital's rule again.

    we get 2a/4 as the limit so a/2 = 3 and a = 6.
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  3. #3
    Senior Member polymerase's Avatar
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    Quote Originally Posted by jenius View Post
    Use L'Hopital's rule.

    you get (0+b+c+d)/0

    I think the only way this limit can exist is if b+c+d = 0

    we then get the indeterminate form 0/0

    Use L'Hopital's rule again.

    we get 2a/4 as the limit so a/2 = 3 and a = 6.
    So is 6 the final answer?
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  4. #4
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    Unless I made a mistake somewhere, 6 is the final answer.
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