For instance, say a book is titled "Genesis and Its Interpretations". Is it correct to capitalize "its" in the title?
Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question?
Show that $\sqrt{n^2+1}-n$ converges to 0 I want to use the definition of the limit to show that $\sqrt{n^2+1}-n$ converges to 0.  The definition is as follows: if $\sqrt{n^2+1}-n$ converges to 0, then $\forall \epsilon&gt;0$, there exists an $N&gt;0$ such that $n\ge N \implies \mid\sqrt{n^2+1}-n\mid&lt;\epsilon$.  Now I want to start backwords in order to figure out how to pick N. I know:   $\mid\sqrt{n^2+1}-n\mid=\sqrt{n^2+1}-n$   since $n$ is a natural number and $\sqrt{n^2+1}&gt;n$. So I need to pick an N such that $\sqrt{n^2+1}-n&lt;\epsilon$. I tried multiplying $\sqrt{n^2+1}-n$ by $\frac{\sqrt{n^2+1}+n}{\sqrt{n^2+1}+n}$ but that didn't really seem to help.   Do you have any ideas on how to find this N?  Thanks Sort a set of multidimensional arrays by array elements I have a multi-line equation that I want to have matching sized parentheses. The advice I read online was to use \left( equation \right. \\ left. rest-of-equation \right) . However, this syntax leaves first half of the equation unaware of what is in the second half. For example, if you include a square root term after the break, the second parenthesis will be larger than the opening parenthesis. When you are using the aligned environment to split a long equation this can look somewhat offputting.    Compare the top equation to the bottom one. The parentheses match in size for the bottom equation, but the left hand parentheses for the top one is  noticeably smaller.  Top Code:   \begin{aligned}[t]   \gamma_{\text{u}} + \frac{1}{108}   \left(57\gamma_{\text{er}} \right. &amp;+  38\gamma_{\text{se}}\\ &amp; {}\pm  \left.\sqrt{2601 \gamma_{\text{er}}^2 + 3648  \gamma_{\text{er}}\gamma_{\text{se}} + 1444 \gamma_{\text{se}}^2}  \right)   \end{aligned}   Bottom Code:  \begin{aligned}[t] \gamma_{\text{u}} + \frac{1}{16} \left(9\gamma_{\text{er}}  +  6\gamma_{\text{se}} \pm  \sqrt{49 \gamma_{\text{er}}^2 + 76 \gamma_{\text{er}}\gamma_{\text{se}} + 36 \gamma_{\text{se}}^2} \right) \end{aligned} Cannot turn script back on I've got an issue. When (Input.GetMouseButtonUp (0), Speedy script is disabled, thus we cannot enable it again from inside the script like shown below. How can we go around this?  public class  Speedy : MonoBehaviour {  GameObject car;   if (speed == good)     {         GameObject car = GameObject.FindWithTag ("Car");          if (Input.GetMouseButtonUp (0))          {             car.GetComponent&lt;Speedy&gt;().enabled = false;         }          else car.GetComponent&lt;Speedy&gt;().enabled = true;     } } $2\cos^2x=1+\sin x$.  Determine the exact values of $x$ such that $0 \leq x \leq 2\pi$.    I am experiencing problems with factoring this question.  First I started by getting everything on to the left side so: $2\cos^2x-\sin x-1=0$.  Then seeing as there are two trig variable here ($\cos$ and $\sin$), I used the pythagorean identity and replaced $2\cos^2x$ with $1-2\sin^2x$ to make it into a one variable question: $1-1-2\sin^2x-\sin x-1=0$.   By collecting like terms it then becomes $-\sin^2x-\sin x=0$.  Now you could factor these with $0$ and $-1$, but then it creates uneven brackets so this musn't work.  I don't think the quadratic formula is necessary, but I am wondering if this could be treated as a difference of squares question.    If you replace the $\sin x$ and make the question into $-x^2-x=0$ it is a little easier to look at, however I am not sure if this is the right approach.  If someone could please clarify my answer, that would be appreciated! Windows 7 task bar at autohide, make it totally disapear? My desktop look is empty so all I have is a nice wallpaper. My Windows taskbar has the "Taskbar Appearance" setting to "Auto-hide the taskbar". Although hidden, it leaves a thin top layer so you can still see it a bit, and where the pinned shortcuts are. Is it possible to totally have it hidden without a trace? This is a serious question. It really bugs m. What is the simplest and most robust way to get the user's current location on Android? As I understand this, firewalls (assuming default settings) deny all incoming traffic that has no prior corresponding outgoing traffic.  Based on  and , reverse SSH tunneling can be used to get around pesky firewall restrictions.  I would like to execute shell commands on a remote machine. The remote machine has its own firewall and is behind an additional firewall (router). It has an IP address like 192.168.1.126 (or something similar). I am not behind a firewall and I know the remote machine's IP address as seen from the Internet (not the 192.168.1.126 address). Additionally, I can ask someone to execute ssh (something) as root on the remote machine first.  Could anyone explain me, step by step, how reverse SSH tunneling works to get around the firewalls (local and remote machines' firewalls and the additional firewall between them)?  What is the role of the switches (-R, -f, -L, -N)? Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$ How do we prove that this set is not manifold? This question has been asked before, at least twice by people who were trying to cheat on the PROMYS Europe 2020 Application, and once in a  because the OP showed no effort. I haven't been able to solve it, so I'm going to to ask it again.  PROMYS applications have closed, and I hope the effort shown below is enough to keep this question from being closed.     The Mathematical Forest is grown in a two-dimensional plane, where   trees can only grow on points with integer coordinates. To start with,   there are no trees at all. The foresters plant the first tree at   $(0,0)$. Each year, they carry out tree planting according to the   following rule. If there is a tree on the point (𝑚,𝑛) but there are   no trees on the points $(m+1,n)$ and $(m,n+1)$, then they can choose   to remove the tree on $(m,n)$ and plant new trees on the points   $(m,n+1)$ and $(m+1,n)$. For an integer $k\geq1$, the $k$th diagonal   consists of all points $(m,n)$ with $m+n=k−1$. Is it possible for the   foresters to arrange their planting so that eventually there are no   trees on the first $2$ diagonals? What about the first $3$ diagonals?    $4$ diagonals? Can you generalize?   It's easy to get to a position with no trees on the first two diagonals.  (It only takes $4$ plantings.)  I can prove it's impossible to reach a position with no trees on the first $4$ diagonals, and I believe it's impossible to reach a position with no trees on the first $3$ diagonals, but I can't prove it.  For the $k=4$ case, I used a pagoda function, as in a peg solitaire problem.  For $k=1,2,3,\dots$ define the potential of a tree on the $k$th diagonal as $\frac1{2^{k-1}}$, and the potential of the forest as the sum of the potentials of all the trees in it.  When a tree of potential $\frac1{2^{k-1}}$ is removed, it is replaced by $2$ trees of potential $\frac1{2^k}$ so the potential of the forest never changes.  Initially, the potential of the forest is $1$.  Since there are $k$ trees on diagonal $k$, the potential of all points beyond the fourth diagonal is $$\sum_{k=5}^\infty\frac k{2^{k-1}}=\frac34&lt;1,$$ so it is impossible that there are no trees on the first $4$ diagonals.  The potential of the fourth diagonal is $\frac12$, so this argument doesn't show that it's impossible to have no trees on the first $3$ diagonals.  I've done a lot of experimenting, though, and I believe that the statement is true.  (I even wrote a little computer game so I could experiment quickly.)  The best I've been able to do is to get down to one man on the third diagonal.   The black circles are trees eligible for removal, and the gray circles are other trees.  You can see that there is a "traffic jam" in front of the lone tree on diagonal $3$, and there seems to be no way to clear it.  I've been trying to come up with an argument that reflects this traffic jam, but I haven't been at all successful. We know that after $n$ removals there are $n+1$ trees, and I've been trying to prove somehow that they can't all be sufficiently far from the origin to allow all trees to get past diagonal $3$, but I haven't come close.   In the diagram above, if the tree at $(1,1)$ were moved to $(0,2)$, and the tree at $(1,2)$ were moved to $(2,0)$, then it would be possible to remove the tree at $(0,2)$, emptying the second diagonal.  In the fictitious position, we still have one tree on diagonal $2$ and two on diagonal $3$.   So, I think an argument along the lines I was trying cannot just be concerned with the distance from the origin; it must somehow take into account how the trees interfere with one another.  I haven't been able to do this.    I'd be grateful for solutions, hints, or counterexamples.  I wasn't really sure what tags to attach.  Please add any that seem appropriate. Best book of topology for beginner? I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one.. (java) ObjectInputStream deserializing wrong version of object Test to see if the title length requirement can be circumvented by appending lots of dots. Does it make a difference if your URL path ends in a trailing slash or not? Does it make any difference to SEO ratings what-so-ever if your url has a trailing slash:  http://www.example.com/some/slug/paths/   as opposed to one that does not:  http://www.example.com/some/slug/paths Wrong nameserver set by resolvconf and NetworkManager I am working on an app that allows customers to upload images, video, (even gif) into my app. Once the case is processed on my app, I want to place those media files into Salesforce. I have a case record that I would this attached to.   I see multiple records can be added in Rest , and that files can be added to notes and attachments. Can I upload multiple notes and attachments in a single rest call? If development on the Stack Exchange iOS/Android apps has ceased indefinitely, what should we do to their bug reports and feature requests? It's been a while since the Stack&nbsp;Exchange team last had an iOS or Android developer, and the development job on the apps have not had any insights for years.  That, however, doesn't deny the fact that there are still many users to them. As a consequence, people are continuing to submit bug reports and sometimes feature requests about them.  If development on iOS/Android apps has ceased indefinitely, what should we do to their bug reports and feature requests?  Are we going to keep them with the hope that development on apps will resurrect one day, or just ignore them and telling users that development has frozen? Can I have too many mods? I found a lot of mods that make thinks lighter, and add mark and recall, and a basement I like. They are all on Steam, and what I want to know is if I can have too many? Will they all work together? Or should I just leave them alone? I am facing problem to enable wifi on my Lenovo G50-30 Below are the command out put please help me out   lspci | grep -i wireless:  02:00.0 Network controller: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter     nm-tool:  NetworkManager Tool  State: disconnected  - Device: eth0    Type:              Wired   Driver:            r8169   State:             unavailable   Default:           no   HW Address:        28:D2:44:81:36:0B    Capabilities:     Carrier Detect:  yes    Wired Properties     Carrier:         off   - Device: wlan0   Type:              802.11 WiFi   Driver:            rtl8723be   State:             unavailable   Default:           no   HW Address:        14:2D:27:21:8D:47    Capabilities:    Wireless Properties     WEP Encryption:  yes     WPA Encryption:  yes     WPA2 Encryption: yes    Wireless Access Points      nmcli nm:  RUNNING         STATE           WIFI-HARDWARE   WIFI       WWAN-HARDWARE   WWAN       running         disconnected    disabled        disabled   enabled         disabled       sudo rfkill list:  0: ideapad_wlan: Wireless LAN     Soft blocked: no     Hard blocked: yes 1: ideapad_bluetooth: Bluetooth     Soft blocked: no     Hard blocked: yes 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no 3: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no