`f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)`

If f(x)=(2cosx-sin2x)/((pi-2x)^(2)) , g(x)=(e^(-cosx)-1)/(8x-4pi) h(x)=f(x) for x lt pi/2 h(x) = g(x) for x gt pi/2 then which of the following holds?

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

If f(x)={((sin(cosx)-cosx)/((pi-2x)^2) ,, x!=pi/2),(k ,, x=pi/2):} is continuous at x=pi/2, then k is equal to

Let f(x)={((1+cosx)/((pi-x)^(2)).(sin^(2)x)/(ln(1+pi^(2)-2pix+x^(2))),x ne pi),(lambda, x=pi):}

Let f(x)={((1+cosx)/((pi-x)^(2)).(sin^(2)x)/(ln(1+pi^(2)-2pix+x^(2))),x ne pi),(lambda, x=pi):}

Let f(x)={{:(((1-cosx)/((2pi-x)^(2)))((sin^(2)x)/(log(1+4pi^(2)-4pix+x^(2)))),:,xne2pi),(" "lambda,:,x=2pi):} is continuous at x=2pi , then the value of lambda is equal to

Let f(x)={{:(((1-cosx)/((2pi-x)^(2)))((sin^(2)x)/(log(1+4pi^(2)-4pix+x^(2)))),:,xne2pi),(" "lambda,:,x=2pi):} is continuous at x=2pi , then the value of lambda is equal to

If f(x)=|{:(2cos^(2)x,sin2x,-sinx),(sin2x,2sin^(2)x,cosx),(sinx,-cosx,0):}|" then "int_(0)^(pi//2)[f(x)+f'(x)]dx=