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Can I safely use my camera with a external power supply?
Does Wolfram Mathworld make a mistake describing a discrete probability distribution with a probability density function? Why are some muggles allowed to know of the magical world? Can you restore log file backups to a mirror database after failure? Purely a theoretical question as I've been considering possible DR scenarios...  In this scenario:   The link between a principle and a mirror server becomes unavailable for a period of time (e.g. network outage) Incremental log backups are still being taken during this time Then the principle database fails and is unrecoverable   Is it possible to restore the incremental log backups onto the mirror to bring it up to date and back online, or would you need to start from scratch with a restore of a full backup?  Depending on the size of the database the difference could be hours of downtime so it would be nice to know.  I'm predominantly interested in SQL Server 2008 R2 and 2012 but other people may be interested in other versions if there's a difference. Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$. Let $f$ be a real-valued function continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose that $\lim_{x\rightarrow a}f'(x)$ exists. Then, prove that $f$ is differentiable at $a$ and $f'(a)=\lim_{x\rightarrow a}f'(x)$.    It seems like an easy example, but a little bit tricky. I'm not sure which theorems should be used in here.    ==============================================================  Using @David Mitra's advice and @Pete L. Clark's notes I tried to solve this proof. I want to know my proof is correct or not.  By MVT, for $h&gt;0$ and $c_h \in (a,a+h)$ $$\frac{f(a+h)-f(a)}{h}=f'(c_h)$$ and $\lim_{h \rightarrow 0^+}c_h=a$.    Then $$\lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}=\lim_{h \rightarrow 0^+}f'(c_h)=\lim_{h \rightarrow 0^+}f'(a)$$   But that's enough? I think I should show something more, but don't know what it is. Integral representation of Euler's constant Prove that : $$ \gamma=-\int_0^{1}\ln \ln \left ( \frac{1}{x} \right) \ \mathrm{d}x.$$  where $\gamma$ is Euler's constant ($\gamma \approx 0.57721$).    This integral was mentioned in  as in  , but the solutions I've got uses corollaries from . Can you give me a simple solution (not using much advanced theorems) or at least some hints. How to favorite a question from Android app? Date manipulation Function SSJS I want to delete the records from Data Extension based on Date Field in my DE i.e. I want to delete record which were created date before 30 days.But I didn't find date manipulation function in SSJS like dateadd() in ampscript SSH login without password with kerberos 'The average person' or 'an average person'? LaTeX macro expander Integral $\int\!\sqrt{\cot x}\,dx $ What is the difference between these two ways to calculate average velocity? Average velocity:  $$v_{\rm avg,1}=\frac{v_{\rm final}+v_{\rm initial}}{2}$$   and average velocity:   $$v_{\rm avg,2} =\frac{\rm total\;displacement}{\rm time \;taken}=\frac{\Delta x}{\Delta t} $$  What is the difference between them and when do we use them? Is it possible to adjust desktop monitor brightness like on laptops? Yes all desktop monitors have separate menu for it. But is it possible to change this to something like Winkey+(F1..F12)?    Monitor is connected via VGA or DVI cable.   OS: Ubuntu 14.04 Desktop monitors Does there exist a continuous bijection from $(0,1)$ to $[0,1]$? Of course the map should not be a proper map. What are your thoughts on epigraphs in theses? I am wondering if there is a general consensus as to the suitability of epigraphs in a thesis, either a single one at the start of the document, or an appropriate quote to begin every chapter.  For example, at the start of a technical chapter describing some code, I could write     Beware of bugs in the above code; I have only proved it correct, not tried it. - Donald E. Knuth   I am lucky to have complete freedom over how I choose to typeset my thesis (Master's thesis in astronomy) and I like the idea of a thematic quote to begin a chapter. However, I am wary of seeming unprofessional or tacky so I am curious to get some more thoughts on the matter. Pre-image of a measurable set A is always measurable? Would it be possible for some to bend two elements? After reading this question  While it seems that it would break one of the rules of the show, that only the avatar can master all four elements. There would also be good reasons as to why someone couldn't learn all four, there is always the opposing element that is hardest for the Avatar to learn. I don't see any reason why someone couldn't learn to bend two elements (not master, but just bend since Thadeus's Answer  to the previous question is apparently the Definitive Answer on the subject.)    Many benders do learn to bend beyond their element such as Toph becoming a metal bender and Katarra bending blood. Now metal is considered part of the Earth but so is sand and it seems that sand is moved more like water. Iroh was able to adapt a water bender technique to fire bending which means it is possible to learn and use different bending styles. Also Iroh spent time connecting to the spirit world and that seems to be the main reason the Avatar is able to bend all 4 elements. So if someone was connected to the spirit world or even their past life that would fulfill that requirement.   Would it be possible to bend two elements?  There do seem to be times where it has been done in the series such as bending mud which is both Earth and Water. And there would definitely be limits such as a Earth bender couldn't bend Air and a Water bender couldn't bend Fire. But why couldn't a Fire Bender learn to bend Air. They both use breath control as a main focus of their bending. It also states on the Energybending wiki entry that all bending used to be done as an inner bending but that it became element bending.   So with new bending techniques being formed all the time, already stated used of combined elements being used, an assumed spiritual connection to a past life or a spiritual journey been taken, energybending rediscovered is it possible that two elements could be bent by one bender who is not the Avatar? Why is boiling water loud, then quiet? Water in my electric kettle makes the most noise sixty to ninety seconds before the water comes to a full boil. I have been fooled many times by the noisy kettle, only to discover that the water was not yet hot enough for tea. The kettle is only at a full boil after the noise has subsided.    I have noticed the same phenomenon with many other kettles, including conventional kettles on kitchen ranges; it is not a peculiarity of this electric kettle.  Why does the boiling become quieter as the water reaches full boil? Detection of the Electric Charge of a Black Hole Coloring arrows in \xymatrix