# Thread: Finding sum of constants in limits

1. ## 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?

Thanks!

2. 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.

3. Originally Posted by jenius
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?

4. Unless I made a mistake somewhere, 6 is the final answer.