The values of awb and c such that limx→0 axex−blog⁡(1+x)+cxe−xx2sin⁡x=2

limx→0ax(1+x+x22!+...)−bx−x22+x33−...+   cx1−x1!+x22!+x33!x2x−x33!+x55!  Coefficient of x&x2=0 and coefficient of x3=2⇒a-b+c=0,a+b2-c=0 and a2-b3+c2=2Solving the above equations, we get a=3, b=12 and c=9