Let `f(x) = secx*f'(x), f(0) = 1,` then `f(pi/6)` is equal to (i)`1/sqrte` (ii)`sqrte` (iii)`e^(3/2)` (iv) `1/(2sqrte)`

Let f(x) =intsqrtx/((1+x)^2)dx(xge0) . The f(3) - f(1) is equal to :

If f(x)=((3x+1)(2sqrt(x)-1))/(sqrt(x)) , then f'(1) is equal to (i) 5 (ii) -5 (iii) 6 (iv) (11)/(2)

Let f(x)=(sin^(2)pix)/(1+pi^(x)). Then, int[f(x)+f(-x)]dx is equal to

Let f(x)=1+2sin((e^(x))/(e^(x)+1))x>=0 then f^(-1)(x) is equal to (assuming fis bijectve)

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

Let f(x)={[((e^(3x)-1))/(x),,x!=0],[3,,x=0]} then 2f'(0) is

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

Let f(x)=int(1)/((1+x^(2))^(3//2))dx and f(0)=0 then f(1)=