misconception of full wave and half wave filter rectifiers
Is full wave rectifier better than half wave one?
How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$? Let $a\geq 0$ and $ b\geq 0$. Prove that $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$. [Hint: Use the identity $(a^n -b^n)=(a-b)(\sum_{i=0}^{n-1}a^ib^{n-1-i})$]    I need some help! I cannot do it even with the hint... :( How to get my own IP address and save it to a variable in a shell script? Objective-C - When to use 'self' Difference between shadowing and overriding in C#? I'm looking to find records in a table that match a specific number that the user enters.  So, the user may enter 12345, but this could be 123zz4-5 in the database. I imagine something like this would work, if PHP functions worked in MySQL. SELECT * FROM foo WHERE preg_replace(&quot;/[^0-9]/&quot;,&quot;&quot;,bar) = '12345'  What's the equivalent function or way to do this with just MySQL? Speed is not important. How to show that all points are inside of unit circle? There are $n$ points on the plane. Any $3$ of them are inside of a unit circle. How to show that all points are inside of unit circle?  It is needed to prove that if there is a unit circle for each $3$  points which contains them, there is also a unit circle which contains all $n$ points. It is possible to press ⎇ Backspace on macOS in order to delete the previous word (left of the cursor), and ⌘ Backspace to delete the previous line (left of the cursor). If you have an external keyboard with a "delete" key (or the "forward delete key"), or are able to emulate the delete key via software, it is possible to press ⎇ Delete to delete the word to the right of the cursor. However, perhaps surprisingly, it is not possible to press ⌘ Delete in order to delete the line to the right of the cursor.  Now, I have only been able to make this possible by emulating a ⌘⇧→ and then a Backspace with BetterTouchTool. However, I want to avoid doing something like this because BTT does not work at a "low enough level" for me – that is to say, the action is not entirely reliable.  Is there any official macOS way to delete the line to the right of the cursor? Prove universal morphism is unique up to unique isomorphism. I'm following along Wikipedia page() on universal property, and this seems it should be trivial, but I couldn't finish the proof.  The definition I am working with:   The problem   So I want to prove that if $(A, u)$ and $(A', u')$ are universal morphism from $X$ to $F$, then there exists unique isomorphism $k: A \rightarrow A'$ such that $u' = F(k) \circ u$.   My attempt:   For any $B \in C$ and $f: X \rightarrow F(B)$, there exists unique $h: A \rightarrow B$ such that $f = h \circ u$.  Letting $B = A'$ and $f = u'$, we see that there exists unique $k: A \rightarrow A'$ such that $Fk \circ u = u'$.  This shows existence and uniqueness. We only need that $k$ is isomorphism, but this is the part I cannot prove.   Similarly, there exists unique $k': A' \rightarrow A$ such that $Fk' \circ u' = u$.  Plugging into each equation, we get  $$Fk \circ Fk' \circ u' = F(k \circ k') \circ u' = u'$$  $$Fk' \circ Fk \circ u = F(k' \circ k) \circ u = u$$  but this of course doesn't imply $F(k \circ k') = id$, so it seems useless.   Thanks for your help! Is it okay to use the phrase "try and"? Is it grammatically correct? e.g. "I will try and answer ..." I read the following sentence in book (App).     I will try and answer any questions you ask.   Why don't they use the following? (it is much common):     I will try to answer any questions you ask.   Is there any difference in meaning?  Update:  I noticed that a lot of books and news websites are using this phrase:        Although Katty will try and answer as many questions as she can.    He puller would have a chance to try and answer the question on her own ... Word for seeing both sides of an argument For some reason my Steam just broke today after working perfectly since I installed it a few days ago.  It was originally installed via the deb from the Steam site. So I uninstalled that using the Ubuntu Software Center. Then I installed steam-launcher. When I run it from the menu it does nothing at all. When I go through terminal it gives this message, no error:  $ steam/usr/bin/steam:  line 196: /home/andrew/.local/share/Steam/steam.sh: Success   So I purge-removed it and removed the .steams directory from my home directory but on re-installation its the same story.  I am using Xubuntu 12.10 64bit.  It appears that steam .local/share/Steam/steam.sh is blank. What is it meant to have in it? I am so confused with how reinstalling it doesn't fix it. I want to clear a element from a vector using the erase method. But the problem here is that the element is not guaranteed to occur only once in the vector. It may be present multiple times and I need to clear all of them. My code is something like this:  void erase(std::vector&lt;int&gt;&amp; myNumbers_in, int number_in) {     std::vector&lt;int&gt;::iterator iter = myNumbers_in.begin();     std::vector&lt;int&gt;::iterator endIter = myNumbers_in.end();     for(; iter != endIter; ++iter)     {         if(*iter == number_in)         {             myNumbers_in.erase(iter);         }     } }  int main(int argc, char* argv[]) {     std::vector&lt;int&gt; myNmbers;     for(int i = 0; i &lt; 2; ++i)     {         myNmbers.push_back(i);         myNmbers.push_back(i);     }      erase(myNmbers, 1);      return 0; }   This code obviously crashes because I am changing the end of the vector while iterating through it. What is the best way to achieve this? I.e. is there any way to do this without iterating through the vector multiple times or creating one more copy of the vector? How can I get a specific line from a file? \xymatrix undefined What program can be used to package software into one executable? StringTokenizer? Convert the String to a char[] and iterate over that? Something else? Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$ Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You. An exciting new feature is described in the :        There is a new NPC housing interface that can be used to assign living areas to NPC’s. This interface will also tell you if a room is missing any requirements.      How can this interface be accessed? Remove the most popular tag from the title using JavaScript So, I see that  to fight site scrapers. But, this is harmful to User Experience. With browsers like Google Chrome, all I can see is the first few characters of the title, and it becomes annoying to try to find the right tab.  So, my request: Can you remove the tag from the &lt;title&gt; using JavaScript? Crawlers will still see the SEO-friendly &lt;title&gt;, and users won't have their user experience hampered by it. We all win. IP tables - changes not persisting