Prove that \$ f (x) = sum_ {n = 1} ^ { infty} e ^ {- nx} sin {(n pi x)} \$ infinitely differentiable on \$ (0, infty) is \$.

Prove that $$f (x) = sum_ {n = 1} ^ { infty} e ^ {- nx} sin {(n pi x)}$$ is infinitely differentiable on $$(0, infty)$$,

I have succeeded in proving only one time differentiability using a nearly uniform convergence of derivative series.

: nx

BlackHatKings: General PPC discussion
Posted by: Jamesreimb
Post Time: June 19, 2019 at 18:38.

Value from \$ lim_ {x to infty} frac {lnx ^ n-[x]} {[x]} \$

Find the value of $$lim_ {x an infty} frac {lnx ^ n-[x]} {[x]}$$where n is a natural number and [.] represent the largest integer function

I can not solve this problem.

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File size: 1.3 GB

Siemens PLM Software has released the first maintenance package of the PLM NX 12 software, a major release with significant new features across the product. With the release of NX 12, Siemens PLM is still looking for innovation to improve an already mature system.
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Samsung Galaxy NX Mirrorless Digital Camera 20.3MP (Android 4.4) Poor Wifi / Mobile Signal Problems

Does anyone have this camera that can help troubleshoot Wifi / Mobile issues?

I have this camera, it worked well. The wireless and mobile reception was good. After use, they have dropped dramatically, so that the transfer rates of images over Wi-Fi or mobile networks are less than 1 MB / s

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I did a factory reset and reset and tried to assign static and dynamic IP addresses.
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Siemens NX software is a flexible and powerful integrated solution that helps you deliver better products faster and more efficiently. NX offers the next generation of design, simulation and manufacturing solutions that help businesses realize the value of the digital twin.
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Intel:
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Uniform convergence of \$ U_n (x) = sum_ {n = 0} ^ {+ infty} (-1) ^ n ln (1 + frac {x} {1+ nx}) \$.

We consider the function series:

$$U_n (x) = sum_ {n = 0} ^ {+ infty} (-1) ^ n ln (1 + frac {x} {1 + nx})$$ , $$x geq0.$$

1. Prove that $$U_n$$ is convergent.

2. Study the unified convergence of $$U_n$$,

3. Study the normal convergence.

4. We consider $$U (x) = sum_ {n = 0} ^ {+ infty} (-1) ^ n ln (1 + frac {x} {1 + nx})$$, Prove that $$U (x)$$ is of class $$C ^ 1$$,

5. To calculate $$U & # 39; (x)$$,

1. We have: $$(-1) ^ n ln (1 + frac {x} {1+ nx}) sim (-1) ^ n frac {x} {1+ nx} leq frac {(-1) {n} implies$$ $$U_n (x)$$ converges.

2. I do not know how to ask this question because I do not know the value of the sum $$U_n (x)$$ to calculate : $$lim sup | U_n (x) – l |$$, How can you tell if the series has a consistent convergence?

3. For normal convergence we have: $$sum sup | U_n (x) | = sum ln (1 + frac {1} {n}) = + infty$$

therefore $$sum U_n$$ does not converge normally.

1. $$U (x)$$ is of class $$C ^ 1$$ means that it is differentiable and its derivative is continuous. If $$sum U_n$$ converges uniformly, $$U$$ I have the same qualities, but how can I prove that $$U$$ is of $$C ^ 1$$ without counting $$U & # 39; (x)$$ first? I am confused because I am asked to calculate in the last question $$U & # 39; (x)$$, Is there a way to derive this from a unified convergence?