Hello guys, I am trying to prove that the function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(u)=-\frac{1}{(1+u)^2}[/tex]

is Hölder continuous for [itex]-1<u \le 0[/itex] but I am stuck. Here is what I have done:

If [itex]|u_1-u_0| \le \delta[/itex] then

[tex]\left|-\frac{1}{(1+u_1)^2}+\frac{1}{(1+u_0)^2}\right| \le \left|\frac{(u_1+u_0)+2}{(1+u_1)^2(1+u_0)^2}\right||u_1-u_0| \le \frac{2|u_1-u_0|}{(1+u_1)^2(1+u_0)^2}[/tex]

and I dont know how to continue... Any suggestions?

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# Hölder Continuity

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