Show that `tan^(-1)x > x/(1+(x^2)/3)ifx in (0,oo)dot`

Show that ln(1+x)>x-(x^(2))/(2)AA x in(0,oo)

Differentiate tan^(-1)((2x)/(1-x^(2))) with respect to sin^(-1)((2x)/(1+x^(2))), if x in(1,oo)

Differentiate tan^(-1)((2x)/(1-x^(2))) with respect to sin^(-1)((2x)/(1+x^(2))), if x in(-oo,-1)

int_ (0) ^ (oo) (x tan ^ (- 1) x) / ((1 + x ^ (2)) ^ (2)) dx

int_(0)^(oo)(tan^(-1)x)/(1+x^(2))dx

Show that f(x)={12 x-13 ,2x^2+5, ifxlt=3ifx >3 is differentiable at x=3 . Also, find f^(prime)(3)dot

Show that lim_(xrarr0)(1)/(|x|)=oo.

If xy=1+a^(2) then show that tan^(-1)((1)/(a+x))+tan^(-1)((1)/(a+y))=tan^(-1)((1)/(a)),x+y+2a!=0

If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is independent of ' x ' then (a)x in (-1,1) (b) x in (-oo,-1) (c)x in [1,oo) (d) x in (0,1)

Differentiate tan^(-1)((2a^x)/(1-a^(2x))), a >1, -oo