`("lim")_(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)}` is equal to `pi` (b) `2pi` (c) `pi/2` (d) none of these

tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y) is equal to (A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

If x<0,\ y<0 such that x y=1 , then tan^(-1)x+tan^(-1)y equals pi/2 (b) -pi/2 (c) pi (d) none of these

int_(0)^(oo)(xdx)/((1+x)(1+x^(2))) is equal to (A)(pi)/(4) (B) (pi)/(2)(C)pi(D) none of thesel

tan((pi)/(4)+(1)/(2)cos^(-1)x)+tan((pi)/(4)-(1)/(2)cos^(-1)x),x!=0 is equal to x( b) 2x( c) (2)/(x) (d) none of these

If x_(1)=2tan^(-1)((1+x)/(1-x)),x_(2)=sin^(-1)((1-x^(2))/(1+x^(2))) where x in(0,1), then x_(1)+x_(2) is equal to 0 (b) 2 pi(c)pi pi(d) none of these

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

(lim)_(x->oo)((2tan^(-1)x)/pi)^x