Given that `lim_(xtooo) ((2+x^(2))/(1+x)-Ax-B)=3`
What is the value of B?

Options

A. `-2`
B. 3
C. `-4`
D. `-3`

Answer

C

Explanation

`underset(xtooo)lim((2+x^(2))/(1+x)-Ax-B)=3`
`impliesunderset(xtooo)lim((2+x^(2)=Ax-B-Ax^(2)-Bx)/(1+x))=3`
`impliesunderset(xtooo)lim[((1-A)x^(2)-(A+B)x+2-B)/(1+x)]=3`
Applying L' Hospital rule,
`2x(1-A)-(A+B)=3`
Comparing coefficients
`2(1-A)=0`
`:.A=1and-(A+B)=3`
`:.B=-3-1=-4`
`A+B=-3`
`A=1,B=-4`