The correct option is B 16
Let, L=limx→0ex+e−x+2cosx−4x4
Using series expansion,
ex=1+x+x22!+x33!+................
e−x=1−x+x22!−x33!+................
and, cosx=1−x22!+x44!−x66!+..............
∴L=limx→02(2+x22!+x44!+x66!+...........)+2(1−x22!+x44!−x66!+...........)−4x4
=2(14!+14!)=16