Question

Functia f:[-pi/2,pi/2]->R f(x)= rad(1-cos^2 x)/ (1-cosx), x€[-pi/2,pi/2]\{0} si f(x)=a,x=0 este continua pt a=?

Answer 1

f(x)=√(1-cos2x)/(1-cosx)=√2*sin²x/2sim²(x/2)=√4sin²(x/2)*cos²(x/2)/sin²(x/2)=
2√cos²x/2=2cosx
f(x)={2cosx  x∈[-π/2,π/2]\{0}
{a  ,x=0
ls  x<0 ,x→0, f(x)=2
ld x>0, x→0 f(x)=2
Functia  e  continua  daca  ls=ld=f(o)=2 =>a=2