If _ x [ x^2+x+1 x+1 - ax - b ] = 3 , then a - b = ...

Step-by-step solution

The given limit is _ x [ x^2+x+1 x+1 - ax - b ] = 3 Taking the LCM, we get: _ x [ x^2+x+1 - ax(x+1) - b(x+1) x+1 ] = 3 _ x [ (1-a)x^2 + (1-a-b)x + (1-b) x+1 ] = 3 For the limit to be finite as x , the degree of the numerator must be less than or equal to the degree of the denominator. Therefore, the coefficient of x^2 in the numerator must be zero. 1 - a = 0 a = 1 Substituting a = 1 in the limit expression: _ x [ -bx + (1-b) x+1 ] = 3 Dividing the numerator and the denominator by x : _ x [ -b + 1-b x 1 + 1 x ] = 3