(cos3dx)/(2)+(1)/(x-2)+(2)/(x-1)=(6)/(x)quad x!=1,2,0

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx) is equal to 4 (b) 3 (c) 1 (d) 0

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx) is equal to 4 (b) 3 (c) 1 (d) 0

lim_(x rarr0)((cos x)^((1)/(2))-(cos x)^((1)/(3)))/(sin^(2)x) is

int_(0)^(2)((x-1)^(2)sin(x-1) dx)/((x-1)^(2)+cos(x-1))

If d/(dx) {f(x)}=1/(1+x^2) then d/(dx){f(x^3)} is a) (3x)/(1+x^3) b) (3x^2)/(1+x^6) c) (-6x^5)/(1+x^6)^2 d) (-6x^5)/(1+x^6)

If y=(sin^(-1)x)^(2)+(cos^(-1)x)^(2), then (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx) is equal to 4(b)3(c)1(d)0

(lim)_(x->0)((cos x)^(1//3)-(cos x)^(1//2))/(sin^2x) equals a. 1/12 b. 1/6 c. 1/3 d.1/2

(i) int_0^1 (dx)/sqrt(1-x^2) (ii) int_0^1 (dx)/sqrt(1+x^2) (iii) a int_1^sqrt3 (dx)/(1+x^2) b int_0^1 (dx)/(1+x^2) (iv) int_0^(2//3) (dx)/(4+9x^2) (v) int_0^1 x/(x^2+1)dx (vi) int_2^3 x/(x^2+1) dx