Homework Statement
Show that this function f_{n}(x)= x^{5}+nx-1
has exactly one real zero point and it is in the interval
\left(\frac{1}{n+1},\frac{1}{n}\right)
Homework Equations
By calling the zero point a_{n}
decide if the series \sum \left(-1\right)^{n-1} a_{n}
converges...
The taylor serries for sin (x) = \sum\frac{-1^{n}}{(2n+1)!}x^{2n+1}
and by substituting (pi x^2)\2
we get
\sum\frac{-1^{n}}{(2n+1)!}\left(\frac{\pi\times x^{2}}{2}\right)^{2n+1}
Woow It is a power series now
s(x) =\int \sum\frac{-1^{n}}{(2n+1)!}\left(\frac{\pi\times...
Homework Statement
Find the power series representation for s(x) and s`(x)
integral sin (pi t^2)\2
and which of them is valid ?
Homework Equations
The Attempt at a Solution
I tried to solve this question , but i am not sure
s`(x) = sin (pi t^2)\2...
Thanks
Yes , i think you proof is right
because x arctan x seems to be uniformly cont. because it is bounded between 90, -90
but about cos ln x , if we take the limit of f`(X) = - sin 1\x
the limit when x goes to 0 does not exist .
i think it is enoygh to prove that this function is...
1- the first one if we find f`(x) = 1\x
and if we find the lim when x goes to 0 , then the limit does not exist
So , the function is not uniformly cont. on this interval
right ?
but how can i solve the next one ?
determine if these functions are uniformly continuous ::
1- \ln x on the interval (0,1)
2- \cos \ln x on the interval (0,1)
3- x arctan x on the interval (-infinty,infinty)
4- x^{2}\arctan x on the interval (infinty,0
5- \frac{x}{x-1}-\frac{1}{\ln x} on the interval (0,1)...