Any help? i am going to school is 15 mins
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
now plug in
The result is obviously true for , since for all .
Thus, we consider if
again, since for all , we need not worry about it making our function negative. thus it suffices to show that for . (since that would show that no matter how negative gets, it will always be overwhelmed by the more positive , and thus for all ).
Now, consider the function
we claim that . For consider otherwise that
if , then , which clearly makes no sense
likewise, if , then , again makes no sense. thus,
but that means that which means that . thus, we have proven that for all
QED
if you found f'(x) already, what is your problem here? just plug it in and solve. plug in f'(x) into the left side of the equations in B) and C) and show that when you simplify, you get the right hand side, namely, f(x), the original functionB) 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