Home » Blog » Find values of a and b such that the given limit exists Find values of a and b such that the given limit exists by RoRi March 31, 2016 Find values for the real constants and so that the following limit equation holds: Incomplete. Related
add and subtract x^2 and x, you get an x and it’s integral is zero, now group the numerator to get (a-1)x^2+(b-1)x and add and subtract
(a-1)x+(a-1) you get (a-1) which is why a should be 1 and then you can add and subtract (b-a)/2, one of the parts will be a logarithm and the other arctan, for the limit to exist a must be 1 and note that the arctanx approaches +-pi/2 as x tends to +- infinity
If we do a=1+A and b=1+B yields: x + (Ax^2 + Bx)/(x^2 + x + 1). But x is odd and so we consider only (Ax^2 + Bx)/(x^2 + x + 1).