d school question no. 16, 55, 56 year2008

[Kamal1]

Sir,
I am not able to work out these 3 problems. Please help.

[Khushboo]

Ans-16  Def: A function is said to be linear if
                  f(ax+by) = af(x) + bf(y)  
             Now,apply definition..it implies that g is a linear function, f is not linear i.e option d

Ans-55  For any x positive, lim is 0 (think about it), so option d is correct.  
                         
                           
Ans-56   ( ∫ fn )  is a constant sequence converges to 1, so option c.