`lim_(x->oo) cot^-1x/(cosec^-1x)`

Which of the following limits does not exist ?(a) lim_(x->oo) cosec^(-1) (x/(x+7) (B) lim_(x->1) sec^(-1) (sin^(-1)x) (C) lim_(x->0^+) x^(1/x) (D) lim_(x->0) (tan(pi/8+x))^(cotx)

lim_(x->oo)sin(1/x)/(1/x)

The lim_(x rarr oo)(cot^(-1)(x^(-a)log_(a)x))/(sec^(-1)(a^(x)log_(x)a)),a>0,a!=1 is equal to

cot^(-1)("cosec x"+cotx)

Evaluate the limits lim_(x to 0) (1+sinx)^(2 cosec x)

Evaluate : lim_(x to 0) (1+sinx)^(2 cosec x)

sin^-1(-x) = -sin^-1(x); cos^-1(-x) = pi - cos^-1(x); tan^-1(-x) = -tan^-1(x); cot^-1(-x) = pi - cot^-1(x); sec^-1(-x) = pi - sec^-1(x); cosec^-1(-x) = -cosec^-1(X)

If y = tan^(-1) x + sec^(-1) x + cot^(-1) x + "cosec"^(-1)x , then (dy)/(dx) is equal to