$\frac{x^2 -4}{x-4} \rightarrow -5$ as $x \rightarrow 3$, proving the limit from first principles. ($\delta - \epsilon$).
Prove from first princibles $\frac{x^2-4}{x-4} \rightarrow -5$ as $x \rightarrow 3$
I have a list of Line_item__c which is storing my line items as  List&lt;Line_Item__c&gt; toInsertList = new List&lt;Line_Item__c&gt;();   I am inserting these records in database using the below statement :  List&lt;Database.Saveresult&gt; insertResults=Database.insert(toInsertList, false);   Now the result is stored in insertResults which is of Database.Saveresult type but i want the result in a list of Line_Item__c. How do i do this. If anyone has a idea, it will be of great use. have lived vs have been living Who is allowed to invite people to a Minecraft Realm? Oneboxing a Stack Exchange post using HTTPS does not work When you post a link from Stack Exchange into the chatbox using HTTPS, the link does not onebox. However, if you change the link to HTTP, it works. See the screenshot below:    HTTPS URLs should onebox, too. I have a laptop with a full keyboard (it has numpad), but the laptop is not that big, and because of that the keys are relatively small, which means I am constantly finding myself pressing keys accidentally on the numpad part.  Is there a way to disable specific keys that I simply don't want? Interaction of Invoke Duplicity and Misty Step I have a  for my phone, powered via a micro-usb port. The markings on it indicate that it will accept the typical 5V that nearly every USB port provides, or it will accept 9V for "fast charge".  I was under the impression that USB standards allowed for no more than 5V. My research shows that  has several profiles (up to 20V), and Revision 2.0 Version 1.2 includes a 9V profile.  Now I'm wondering: How can voltages above the usual 5V be provided without worry of damaging an expensive phone when connecting them directly (no wireless pad)? If things are running at different voltages, wouldn't that cause an issue?  In this example, 9V is used for fast charging, but could that 9V be sent to my phone? Do phones have a safeguard for this? The USB standard allows for up to 20V. That's a lot when expecting only 5V. Some "dumb" devices are powered directly off of USB, like cheap LEDs and fans that have no IC. Surely they would blow upon 20V!  I'm guessing there is data exchanged between the power source and the peripheral, ultimately telling the power source whether or not it's okay to provide more than 5V. Some USB charging cables don't have data pins though, which can allow for faster charging. In this case, it seems that not having data pins would be a restriction. Maybe the power source would have to default to 5V?. Unfortunately I cannot find an explicit protocol/explanation of how the different potentials are managed. Elastic IP address on EC2 instance interface without 1:1 NAT Guides on how to install drivers for a Brother all-in-one network printer are either for older devices or are rather complicated as they often involve editing or copying system files in my root directory.  Is there a newer, more convenient way to install the drivers needed? How to trigger workflow from button in O365 I created a script editor webpart. I added a button which start a js function in the onClick event. I would like to start a workflow which is implemented on some list. Is this possible? Prove that: $2^a+3^b<3a+4b$ What are valid values for "data defined" labeling settings? I'm using QGIS 1.8. I'd like to customize label features on an existing shapefile using the new label engine and it's "data defined settings" option. I'd like to know what the attribute table field types should be for each of the settings: All 7 font options, all 2 buffer options, and all 6 position options. Should they all be numeric fields, or some text, or both? I want to create these fields in the attribute table correctly so that I can map them to the label field settings. I can't find information on the proper field types anywhere. Thanks for your thoughts. future or present with when Formal writing: "…for my colleagues and {I/me/myself}."? I'm currently using Cambridge English Advanced 1. It's a book that contains past examination papers, and includes numerous samples of authentic writing. This material helps, candidates and teachers, understand what the examiners are ‘testing’ and how these papers are marked. The assessment covers four categories: content, communicative achievement, organisation and language. Each category is awarded a mark between 1 and 5, so the maximum score is 20, and each mark has a brief note attached by the examiner. Any errors of punctuation, orthography, grammar, appropriacy, and vocabulary are left intact. In fact, there are no corrections because the  ‘examiner’ does not specify where the errors lie. This can be frustrating, even though spelling mistakes are rare at the advanced level, and errors in style, collocation or register are still relatively easy to identify, sometimes I'll read a phrase that forces me to ponder.  Dear Director, [ TEXT ] To conclude, this letter is a polite request to cover the costs of a 2 month language course for my colleagues and me. We would be very pleased if the company would do us this favour. Yours sincerely John Smith  The following marks were awarded Content                    5    blah, blah, … Communicative Achievement  2    blah, blah, …     Organisation               3    blah, blah, … Language                   3    blah, blah, …  I am able to pick out six minor errors in that brief extract, maybe some users will identify more, maybe some will identify fewer, and maybe some will say that the language used is perfectly acceptable. But if I can help a candidate attain that elusive B,  I would be delighted. I am interested in (what could be) the 7th error, emphasised in bold. Because the letter of proposal is formal, I feel the phrase, for my colleagues and me, is jarring. I want to change it to for my colleagues and I, but the antecedent requires an object. You would not say: “This is a request to cover the cost […] for I”. So, why use the subject pronoun I in the expression “my colleagues and…”?  Could I use instead, myself?  Which of the following is preferable in a formal written proposal?    …for my colleagues and me …for my colleagues and I …for my colleagues and myself  EDITED: I found a   of the writing sample (11/11) if anyone is interested.  I've looked at the following question,  Some answers appear to be contradictory, the accepted answer says using  I and me are both grammatical, which in my example is not true. Moreover, there's no mention of myself, as a possible solution, in the question. Sums and products of algebraic numbers How does one go about proving that the sums and products of two algebraic numbers over a field $F$ (say $a,b\in K$, where $K/F$ is a field extension) is also algebraic?   If we call $f_a$ and $f_b$ the min. poly's of $a$ and $b$, then I'm assuming the answer involves such polynomials. Perhaps looking at their roots in splitting fields for both of them? And finding a "big" splitting field, constructed from those two other ones?      In particular, I'd like a way of explicitly constructing the minimal polynomials $\ f_{ab}$ of $ab$ and $f_{a+b}$ of $a+b$.     I read somewhere that $g(x)=\Pi_j\Pi_i (x-\alpha_i\beta_j)$ works for $ab$, where the $\alpha_i$ and $\beta_j$ are the roots of $f_a$ and $f_b$, respectively, but I do not know why $g(x)\in F[x]$.  Similar remarks for $a+b$ Combined flair not updating with badges I've got 28 bronze badges on Stack Overflow, 10 on Astronomy and 15 on Software Recommendations, making it a total of 53. Yet, my combined flair doesn't show that. It just shows the combined badges from my SO and Astronomy SE sites. The reputation has no problem. I can see the correct combined rep. Why is it happening? Is it because Software Recommendations is in private beta?  Here are the flairs (Combined and that from Software Recommendations):     The rep on my combined flair is the sum total of my rep from all three sites. But the badges aren't. Volumetric Lighting is not working I have a simple setup to try out Volumetric Lighting. I have a spot lamp and Volume Scatter set for the World. The cube has a window for the light of the spot lamp.     But no Volumetric Lighting. I have read most questions on this subject. But I have no idea where I am going wrong. BasicTeX - how to identify packages that need to be added after an upgrade How to count occurrences of one field grouped by values of another? Why were there 3-7-9 Rings of Power?