The greatest value of the function `f(x)=(sin2x)/(sin(x+pi/4))` on the interval `(0,pi/2)i s` `1/(sqrt(2))` (b) `sqrt(2)` (c) 1 (d) `-sqrt(2)`

lim_(xto0)(sin2x)/(1-sqrt(1-x))

The value of f(x)=3cos(sqrt ((pi^2)/(16)-x^2)) lie in the interval____

Find the range of the function f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).

The maximum value of cos xsin x+sqrt(sin^(2)x+sin^(2)((pi)/(6))} is

The value of int_(0)^((pi)/(4))sqrt(1-sin2x)dx is

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (sqrt(pi))/6 (b) -sqrt(pi//6) 1//sqrt(6) (d) pi//sqrt(6)

The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greatest integer function, is (a) (-sqrt(3/2),sqrt(3/2)) (b) (-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2)) (c) (-sqrt(5/2),sqrt(5/2)) (d) (-sqrt(5/2),-1)uu(1,sqrt(5/2))