I’m taking MIT ocw single variavle calculus now, and I found I need some books to help with studying. I know Stewart or Thomas calculus is famous for calculus. But I think it’s too huge. And that’s the reason why I have tried to take online lecture. So could you please recommend some calculus books to practice exercises? I want a books which are not huge like Stewart, have some challenge problems, not much focused on analysis. I read some people recommend books, but I think it’s more focused on analysis than calculus.
This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus.
I am using Windows 8 Enterprise on my development machine. Most of the time, I need full administrator for debugging, changing system files, etc.  In Windows 7, setting UAC to "never notify" would disable any administrator prompts. In Windows 8 this is no longer the case. Even with UAC disabled I get prompted to grant programs elevated privileges.  Is there a way disable this behaviour?  Note: I am fully aware of the repercussions. I have antivirus, firewall, etc and am generally quite careful about what I download or install on my machine. Network booting couldn't find kernel image I have a problem with PXE booting. I followed  on the Ubuntu help wiki. But I get an error on client machine:  Could not find kernel image: vmlinuz-3.13.0-24-generic   And now, question. This image should be in pxelinux.cfg folder, am I right? I am trying to solve the following exercise.      Assume that $m$ and $n$ are co-prime positive integers, and that $k$ is a field. Prove that the ideal generated by $x^{m} - {y^n}$ is a prime ideal in $k[x,y]$.   I tried the following approach : Consider the ring homomorphism ${\varphi}:k[x,y]\rightarrow{k[t]}$ defined by $\varphi(x) = t^n$, and $\varphi(y) = t^m$, and extend $\varphi$ to $k[x,y]$ to ensure that it is a ring homomorphism. Then the ideal $(x^m - y^n)$ is clearly contained in the kernel of $\varphi$. It remains to prove the reverse set inclusion. i.e. to prove that this ideal is exactly equal to the kernel of $\varphi$. I don't know how to go about this! pgfplots from file: search path, looking for \graphicspath equivalent Compute: $\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ where $A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n)$ Let $\{a_n\}, {n\geq 1}$, be a sequence of real numbers satisfying $|a_n|\leq 1$ for all $n$. Define  $$A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n),$$ for $n\geq 1$. Then find $\displaystyle\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ .    I proceed in this way  $$\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)=\lim_{n \rightarrow \infty}\sqrt{n}\left[\frac{1}{n+1}(a_1 + a_2 + \cdots + a_n+a_{n+1})-\frac{1}{n}(a_1 + a_2 + \cdots + a_{n})\right]=\lim_{n \rightarrow \infty}\left[{(na_{n+1}-a_1 - a_2 - \cdots - a_n})\frac{1}{\sqrt{n}(n+1)}\right]$$  Please help me to complete from here Ubuntu 19.10 change desktop environment I've installed another desktop environment which I would like to try. I am not sure how to switch to it.  Is there still a button on the log in screen that will switch desktop environments? This same question for previous versions of ubuntu yields screenshots of this button. But I cannot find any button on the log in screen that does this.  So, in ubuntu 19.10, does there exist a button to switch desktop environments? If so, where is it? If not, what is an alternative method to switch desktop environments after I've already installed one?  ██████@████-linux:~$ ls /usr/share/xsessions gnome-flashback-compiz.desktop    ubuntu.desktop gnome-flashback-metacity.desktop   The gear icon does not show up for me, as the answers indicate it should.    Solved. I was not logged out properly. I locked the screen thinking that was logging out. Logging out properly fixed the issue. A word for a symbol which has outlived its origin I am quite sure that there is a word for a symbol which was originated by a real-life, physical prototype but has since then outlived its origin.  Most notable example: the save button with floppy drive on it. Also, to a lesser degree, envelopes in email clients, and so on.  The "anachronism" or "metonymy" are close, but not exactly what I'm searching for. What if the answers of a historical locked question become obsolete? Why would you not want to rollover a previous employer's 401(k) when changing jobs? Are there any valid reasons to not rollover a former 401(k) when changing jobs?  I have several little ones that I never quite got around to rolling together - with an upcoming job change, should they all be combined into my new employer's retirement plan?  If not, what else might be considered? Ability to update profile from the Stack Exchange Android App It would be nice to update the profile page from within the app.  Perhaps not many people update their profiles more frequently, but when required to do so, I would prefer to do it from the app instead of the mobile browser. What is the differences between &> and 2>&1 There are two forms of redirection the standard output and standard error into standard output. But which one is better? and why the &amp;&gt; is considered the perfect?  I can't find what is the differences so that many tutorials and even bash manual state that  &amp;&gt; is better!   So Why shall I use &amp;&gt; and not 2&gt;&amp;1  Mainly using bash shell    EDIT: Thanks for commentors   Only >&amp; works in csh or tcsh  In ksh only 2>&amp;1 works.  dash use >file 2>&amp;1 redirection only  Then which one to use to ensure my script is compatible with other systems whatever the used shells are! Yesterday I read Modern English:A Practical Reference Guide written by Marcella Frank, and she gives a paradigm about tenses on page 50. The page shows tenses in active voice and passive voice; she said these four tenses are exceedingly rare:   shall/will be being offered has/have been being offered had been being offered shall/will have been being offered   Why are these tense so rare? Are they normally replaced by other tenses? Opening a non-utf8 encoded text file I sometimes need to open text files that are encoded in EUC-KR.    man gedit gives:      --encoding           Set the character encoding to be  used  for  opening  the  files           listed on the command line.    This can be used to open specific files with the desired encoding:  gedit --encoding euc-kr readme.txt   However, each file to be opened requires a similar command to be typed.  I can run iconv on the file(s), but then I have to deal with different file versions.    Do I have better options for dealing with non-utf8 text files? Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another. Given a set of $n+1$ numbers out of the first $2n$ natural numbers, $\{1,2,\ldots,2n\}$, prove that there are two numbers in the set, one of which divides the other.  I can't tell if I'm reducing the problem in the right way.  Would it be something like:  Induction Hypothesis: A set of $n+1$ numbers from the first $2n$ natural numbers contains two numbers, one of which evenly divides the other.  Base Case: $n=1$, $\{1,2\}$, 2 is divisible by 1.  Consider a set of $n+2$ numbers, $A$, from the first $2n+2$ natural numbers. There are three cases:   Each number in $A$ is less than or equal to $2n$.  The proof follows from the induction hypothesis. One number in $A$ is greater than $2n$.  The remaining set of $n+1$ numbers must each be less than or equal to $2n$.  The proof follows from the induction hypothesis. $A$ contains both $2n+1$ and $2n+2$. I'm not sure how to solve this case.   I'm working through Udi Manber's Introduction To Algorithms: A Creative Approach for personal development, so in keeping with the spirit of the book, I'm trying to use induction.  Without induction, the question is identical to Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$ I try to solve this problem. I seems to come close to the end but I can't get the conclusion. Can someone help me complete my proof. Thanks          Show that the polynomial $h(x) = (x-1)(x-2)\cdots(x-n) + 1$ is irreducible over $\mathbb Z$ for all $n\ge1$ and $ n\ne4$.      Suppose $h(x) = f(x) g(x)$, then we must have $f(i)g(i) = 1$ for all $i = 1,2,...n$. So both $f(i)$ and $g(i)$ are $1$ or $-1$. In either case, $m(x) = f(x) - g(x)$ has degree smaller than $n$ and have $n$ different roots ($1,2,...,n$). So we must have $m(x) = 0$. Then $h(x) = f(x)^{2}$. So $n$ must be even. Let $n = 2k$. Because $f(x)$ has degree $k$, there are $k$ values from $\{1,2,...,2k\}$ at which $f(x)$ is $1$ and $k$ values at which $f(x)$ is $-1$.  This is where I got stuck. Hope some one can help me solve this. Thanks. It appears that on Server Fault and Super User, the navigation bar and question title have suddenly become misplaced. The same does not occur on SO and mSO, nor on any of the other SE sites I spot-checked.  This is being seen in both Chrome and Firefox and just began occurring within the last few minutes.      What it should look like:      While this was fixed for a few hours, it has returned as of 22:05. Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$ Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous I am looking for a real valued function of real variable that is $n$-differentiable, but whose $n$th derivative is not continuous.  This is my function:  $f_n(x) = x^{n+1} \cdot \sin{\frac{1}{x}}$, if $x \neq 0$ and 0, if $x=0$. $n\in \{0,1,2,\ldots\}$ For example, if $n=0$, $f_0$ it's continuous and non diferentiable in $0$. I'm new to the world of Apple, I bought a new Macbook Pro, mid-2020, Intel i7, 16GB RAM. I'm a developer, I run apps like VS Code, Sublime Text, Slack, Chrome (Multiple Windows), I play videos/songs in the background. I have been keeping a track of the energy consumption on my Mac, and it only runs for 4 hours. I have reset my SMC after I upgraded to Big Sur. Is 4 hours normal? or should I go to the service center? Update on 3 Feb 2021: I submitted my Mac to the Apple service center they said they conducted a few tests and the conclusion was that the battery is fine (I don't know what type of test they did). So I guess I'll be using it on AC Update on 12 Feb 2021: Took it to the service center, they didn't find any issues so I started using Safari for work and my battery has improved by 1 hour on Average. I have a computer with a video card that has no Linux support.  I discovered this issue while trying to use a persistent usb to boot from.   I found that I can boot like that if I change options and edit so as to add nomodeset there (see ).  Also, editing the syslinux.cfg file from my live persistent USB and adding nomodeset in a line there made this setting automatic for booting from the persistent USB.  Can I make a similar edit for proper install from the same live USB?  Is it possible to edit something on the live USB in order to install the SO from it,  -- that is: having automatically the nomodeset setting already there when the installation starts?  My problem is that in order to install I think I already have to have added nomodeset or I'll see nothing on my display. I need a way to be sure that nomodeset it's permanent from the start.