If `y=2^(-2^((1/(1-x)))` , then find `lim_(x->1^+)y`

If y = tan^(-1) ((1+x^2)/(1-x^2)), find y' .

y=2^(1/((log)_x4) , then find x in terms of y.

f(n)=lim_(x->0){(1+sin(x/2))(1+sin(x/2^2)).......(1+sin(x/2^n))}^(1/x) then find lim_(n->oo)f(n)

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Use formula lim_(x->0)(a^x-1)/x=log(a) to find lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)

Let cos^(-1) (4x^(3) -3x) = a + b cos^(-1) x If x in ((1)/(2), 1] , then the value of lim_( y to a)b cos (y) is

f(x)+f(y)=f((x+y)/(1-xy)) ,for all x,yinR . (xy!=1) ,and lim_(x->0) f(x)/x=2 .Find f(1/sqrt3) and f'(1) .

Find the limits lim_(x to 1) (x^2+2)