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

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- Nov 28th 2007, 02:55 PMpolymeraseFinding sum of constants in limits
If a,b,c,d are constants such that $\displaystyle \displaystyle\lim_{x\to{0}}\frac{ax^2+sin\;bx+sin\ ;cx+sin\;dx}{2x^2+3x^3+4x^4} = 3$ what is the value of the sum a+b+c+d?

Thanks! - Nov 28th 2007, 04:00 PMjenius
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. - Nov 28th 2007, 04:04 PMpolymerase
- Nov 28th 2007, 04:55 PMjenius
Unless I made a mistake somewhere, 6 is the final answer.