The value of limx→∞2(x)1/2+3(x)1/3+4(x)1/4+.....+n(x)1/n(2x−3)1/2+(2x−3)1/3+.....+(2x−3)1/n is

Given limx→∞2x1/2+3x1/3+....+nx1/n(2x−3)1/2+(2x−3)1/3+....+(2x−3)1/nlimh→02(1h1/2)+3(1h1/3)+....+n(1h1/n)1h1/2(2−3h)1/2+1h1/3(2−3h)1/3+.....+1h1/n(2−3h)1/n [on  putting x=1h  as x  →∞, h→0] =limh→02+3h(1213)+4h(1214)+.....nh(121n)(2−3h)1/2+h(1213)(2−3h)1/3+.....+h(121n)(2−3h)1/n =2+0+0+0+.....21/2+0+0+0+.......=2