`("lim")_(yvec0)((x+y)sec(x+y)-xsecx)/y is equal to` (a)`secx(xtanx+1)` (b) `xtanx+secx` (c)`xsecx+tanx` (d) none of these

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If y=a e^(m x)+b e^(-m x), then (d^(2y))/(dx^2)-m^2y is equal to m^2(a e^(m x)-b e^(-m x)) 1 (c) 0 (d) none of these

Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to (a) 4x (b) 2x (c) x (d) none of these

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)) ,then (dy)/(dx) is equal to (a) (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (c) (a y)/(xsqrt(a^2-x^2)) (d) none of these

int_(0)^(pi)(x tanx)/(secx+cosx)dx is

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y+z is also equal to (a) 1/x+1/y+1/z (b) x y z (c) xy+yz+zx (d) none of these

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these