If f(x)=1−cos4xx2x<0ax=0 x16+x-4x>0  is continuous at x=0 , the value of a  is

f(x)=1−cos4xx2x<0ax=0 x16+x-4x>0 If f(x)  is continuous at x=0⇒limx→0f(x)=f(0)=aNow, LHL=limx→0−(1−cos4x)x2=a⇒limx→0−4sin4x2x=a ⇒2(4)=8⇒ a=8Also, RHL=limx→0x16+x−4=a⇒limx→0x(16+x+4)16+x−16=8∴ a=8