यदि `lim_(x to oo)((x^(2)+x+1)/(x+1)-ax-b)=4` है, तब

Options

A. `a=1, b=4`
B. `a=1, b=-4`
C. `a=2, b=-3`
D. `a=2, b=3`

Answer

B

Explanation

`lim_(x to infty)((x^2+x+1) - (ax+b )(x+1))/(x+1)` `= 4`

`lim_(x to infty)((x^2+x+1) - (ax^2+ax+bx+b))/(x+1)` `= 4`

`:.` `lim_(x to infty)``( x^m)/(x^n)`

यदि `m > n = infty`

यदि `m < n = 0`

यदि `m = n =` संख्या

अतः
`lim_(x to infty)` `(x^2(1-a)+x(1-a-b)+(1-b))/(x+1)=4`

`a=1`

`lim_(x to infty)``(-bx+1-b)/(x+1)=4`

`:.` `lim_(x to infty)` `(ax+b)/(cx+d)=a/c`

अतः
`-b = 4`

उत्तर `B``(a=1, b=-4)`