Show that f (x) f (y) = f(x+y) , where
`f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)]`.

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] , show that F(x) F(y)=F(x+y) .

Find f'(x) , given f(x)=(cosx)/(1+sinx)

Find lim_(xto0)f(x) , where f(x)={{:((x)/(|x|)","xne0),(0","x=0):}

Evaluate lim_(xto0)f(x) , where f(x)={{:((|x|)/(x)","xne0),(0","x=0):}

If A= |(cos x,-sin x,0),(sinx,cosx,0),(0,0,1)| .Find A^(n) (by mathematical method).

Discuss the extremum of f(x)=sinx(1+cosx),x in (0,pi/2)

If f (x,y) =e ^(2x+3y) find 3f_(x) (0,0) - 2f_(y) (0,0):

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Find the points of discontinuity of the function f, where f(x)={:{(sinx,0lexlepi/4),(cosx,pi/4lt x lt pi/2):}

Let f: RrarrR, where f(x)=sinx , Show that f is into.