I'm assuming we want to know the limit as n approaches infinity....
a) Limit is just the ratio of coefficients on the n^2 terms = 1/ 2
b) Limit of this is 0 since the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator
c) an an = (n^2 -3n + 1) ^2 / (2n^2 + 1)^2 = (n^4 - 6n^3 +11n^2 -6n + 1) / ( 4n^4 + 4n^2 + 1)
Limit = 1/4
The addition of bn doesn't change this since its limit is 0 as we approach infinity