Let `y=1n(1+cosx)^2` . Then the value of `(d^2y)/(dx^2)+2/(e^(y/2))` equal (a)0 (b) `2/(1+cosx)` (c)`4/(1+cosx)` (d) `(-4)/((1+cos"x")^2)`

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

The value of int_(-pi//2)^(pi//2)(x^(2)cosx)/(1+e^(x)) d x is equal to

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x= (5pi)/4 is equal to (a)1 (b)-1 (c)0 (d)4

Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) is __________

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If y= e^(a cos^(-1)x), -1 le x le 1 , show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0 .

G i v e nint_0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integral int_0^(pi/2)(sinx)/(1+sinx+cosx)dx is equal to (a) 1/2log2 (b) pi/2-log2 (c) pi/4-1/2log2 (d) pi/2+log2

If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -2 (c) -6 (d) 0