Question

Prove that lim x tends to zero sinx/x =1 where x is a radian and hence evaluate lim x tends to 0 sin4x/x

Answer 1

l'Hôpital's rule is easiest:

limx→0 sinx=0 and limx→0 x=0, so limx→0

sinx

x

= limx→0

cosx

1

=1