Question

given f(x) = sin2x/(xcosx)
a) find lim f(x)
x->0
B) find lim f(x)
x-> pi/4

Answer 1

a)
Substitute x=0 into f(x) and see:
f(0)
=sin(2*0)/(0*cos(0))
=sin(0)/(0*1)
=0/0 (undefined).

To evaluate the limit, you could use d'Hôpital's rule or make use of the known limit of sin(x)/x=1 to get
lim x->0 sin(2x)/(xcos(x))=2

b)
Substitute x=π/4
f(π/4)=sin(2*π/4)/((π/4)*cos(π/4))
=1/((π/4)*(√2/2))
=4√2 / π