Match the following

Answer

`(4)`

Explanation

`underset(xtooo)lim((x^(3)+x^(2)+x+sinx)/(x^(2)+2cosx)-asinx-bx+c)=4`
`implies" "underset(xtooo)lim((x+1+(1)/(x)+(sinx)/(x^(2)))/(1+(2cosx)/(x^(2)))-asinx-bx+c)=4`
`implies" "underset(xtooo)lim(x+1-asinx-bx+c)=4`
`implies" "underset(xtooo)lim((1-b)x-asinx+1+c)=4`
`implies" "1-b=0,a=0" and "1+c=4`
`implies" "b=1,a=0" and "c=3`