Hey Guys Hope you are Fine!

i have a problem and i need to know the derivation of this:

lim : 1-sin^2x/ x-pi/2

x-->pi/2

For me we should use Hospital so:

Lim: -2sin2x/ 1-pi/2 ? right? and then?

x--->pi/2

and my problem :

f (x) =x + Radical (1 + x ^ 2)

A) proove that x + (Radical) 1 + x ^ 2> 0

B) Calculate derivative of the function f '[i did this],f and proove that radical (1 + x ^ 2) f' (x) = f (x)

Deduisez in that reel for all x, f (x)> 0

C) proove that

(1 + x ^ 2) f '(x) + xf' (x) = f (x)

Thanks a lot