Let f(t)=2/(t+8)  (a) Simplify the following difference quotient as much as possible:  [f(t+h)−f(t)]/h  MY ANSWER (CORRECT): −2/[(t+8)(t+h+8)]  (b) Use your result from (a) and the limit definition of the derivative to calculate  f'(t)=lim_h→zero [f(t+h)−f(t)]/h=  MY ANSWER (CORRECT): −2/[(t+8)^2]  (c) Use your answer from part (b) to evaluate  f'(−3)  MY ANSWER (CORRECT): −2/25  (d) Find the equation of the tangent line to the curve at the point  (−3,f(−3))  y= ?  I have tried the point-slope formula, y−y_1=m(x−x_1), but my answer was incorrect.
Let f(t)=2/(t+8)  (a) Simplify the following difference quotient as much as possible: $$[f(t+h)−f(t)]/h$$  MY ANSWER (CORRECT): $-2 / [(t+8)(t+h+8)]$  (b) Use your result from (a) and the limit definition of the derivative to calculate $f′(t)=\lim_{h → 0} [f(t+h)−f(t)]/h=$  MY ANSWER (CORRECT): $-2 / [(t+8)^2]$  (c) Use your answer from part (b) to evaluate $f′(−3)$  MY ANSWER (CORRECT): $-2 / 25$  (d) Find the equation of the tangent line to the curve at the point $(−3,f(−3))$ y=  I have tried the point-slope formula, $y-y_1=m(x-x_1)$, but my answer was incorrect.
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group. Let G be a group, where $(ab)^3=(a^3)(b^3)$ and $(ab)^5=(a^5)(b^5)$. Prove that $G$ is abelian group.  Thank you in advance. Any help is appreciated. Can some one explain this terminology please I think I understand it but not completely sure.   I think pull down is where you place a resistor between +V and the other component and pull up is where you place the resistor between 0v and the component.    If I am completely wrong then let me know! Finding a closed form for a recurrence relation $a_n=3a_{n-1}+4a_{n-2}$ Consider the sequence defined by $$ \begin{cases} a_0=1\\ a_1=2\\ a_n=3a_{n-1}+4a_{n-2} &amp; \text{if }n\ge 2 \end{cases} .$$ Find a closed form for $a_n$.    I tried listing out examples, but I don't see any common pattern between them.  All solutions are greatly appreciated. What is a good, short, word to describe a software engineer? What should I call a person who write software, computer programs ? I know he/she is a software engineer, can I call him/her as "Coder"? Change Data Type Varchar To Varbinary(max) In SQL Server I want to do the not independent sign in latex without having to install or define new commands (since I am using latexIT and I cannot load new packages).  Currently I use the following sign for independent:  X{\perp\!\!\!\perp}Y   What can I use for X not independent of Y?  I.e., something like this: ? In the same way as you can currently render the active viewport in Open GL? Some aspects of the Workbench renderer look as if they will be very useful for NPR people. Security importance of Key Schedule in Block Cipher Why is it sensical for a proposition with a false antecedent to validate to true? In propositional logic, the statement "If pigs can fly, then elephants can lay eggs." validates to true because the antecedent validates to false.  In other words, given $a \rightarrow b$, if a is false, the entire statement is true. Why?  Just because the antecendent is false doesn't mean that another fact depends on it, right? How to correctly install libpng12-0 on the Ubuntu 19.10? I have an iOS application - an alarm clock. I released it a little over a month ago. Initially it was paid, but when I saw there were virtually no purchases (from 0 to 4 a day), I changed it to be free for a period of time. When it become free, in less than 10 days it has been downloaded more than 30,000 times, and more importantly (I think) it moved much higher in the search results when the user searches "alarm" - it reached 20th place in the results. During that time I also received very good reviews in the AppStore. But today I changed it back to paid, and now when I search "alarm" my app is shown at the bottom of the 4TH PAGE. Given that one page contains 120 apps, this is very bad for me and I don't understand why this happened. Can anyone tell me how does AppStore ranks search results and is there a way to move my app higher in the rankings, please? :) Huge thanks! "need to do" vs "need do" Consider:  I need to do this. I need do this.  My English grammar knowledge tells me that &quot;need&quot; doesn't have the same status as the modal verbs &quot;may&quot;, &quot;can&quot;, &quot;should&quot; and what not. Hence the second usage where two verbs appear consecutively is incorrect. But yesterday, my native English speaking friends (Americans) told me that &quot;I need compute this.&quot; is a perfectly grammatical sentence, and one is simply omitting the &quot;to&quot;. How can this be? Is it a colloquial usage but grammatically incorrect, or is it grammatically correct? If it is grammatically correct, is it because &quot;need&quot; is a semi-modal verb? EDIT: in particular, is it okay to use &quot;need compute&quot; in a scientific paper? EDIT2: the exact phrase that raised the question was &quot;The advantage of this representation is that we need only compute sums and products&quot; I have recently installed a custom ROM and cannot find the Play Store. It seems like all apps that belong to Google are missing.  How can I install the Google Apps Package (Play Store, ...) on my Android device? I would like to create a XeLaTeX layout where  multicol's columns (two in this case, no figures, text only) are tilted where they meet. The lines still should be ordinary lines below each other, but the start/end points of each line should glide a bit each line for it to look something like this:  xxxxxxxxxx  xxxx xxxxxxxxxx  xxxx xxxxxxxxx  xxxxx xxxxxxxxx  xxxxx SECTION   xxxxxx xxxxxxxx  xxxxxx xxxxxxx  xxxxxxx xxxxxxx  xxxxxxx xxxxxx  xxxxxxxx xxxxxx  xxxxxxxx xxxxx  xxxxxxxxx xxxxx  xxxxxxxxx xxxx  SUBSECTION xxxx  xxxxxxxxxx   So not the whole column is tilted, but one gets narrower while the other one gets wider.  I've seen examples using \parshape, but those I found are based that one counts lines and more or less manually defines the shape. I also would need that LaTeX keeps the multicol functionality (page breaks, text flow, ...) and does this automatically on each page for a longer chapter.  How do I create such a layout? If multicol is not easy to mix with this layout, what would be an alternative? We can easily find out if the vectors are dependent or not by finding determinant of matrices formed from the vectors. But if the matrix is not a square matrix, we cannot find the determinant. Then how do we know if the vectors are linearly independent? Show that the series $\sum(\exp(\frac{(-1)^n}{n})-1)$converges, but not absolutely. Show that the series converges, but not absolutely. $\sum_{n=1}^{\infty}( $exp$(\frac{(-1)^n}{n})-1)$.   My Try:  Let $a_n=$exp$(\frac{(-1)^n}{n})-1$. I was going to use alternating series test because the sequence $\{a_n\}$ is alternating. But $\{|a_n|\}$ is not decreasing to $0$. So, I am stuck now. Can anybody please give me a hint? "To mentor someone during a project" vs. "to mentor someone on a project" ..., whom I mentored during his final semester's project.   ..., whom I mentored on his final semester's project.      Which of these two is grammatically correct? Since I am not talking about the final semester but the final semester's project, I am not very sure about during. Can someone help me with this? Are the PUT, DELETE, HEAD, etc methods available in most web browsers? Everybody who is using Lightroom probably has seen this. After importing RAW files, Lightroom shows a preview, but contrast and color of the preview change after a few short seconds to a slightly different view.  For some users the change is small, for others the change is huge. Colors are different (read: wrong), contrast is off.  Rumor says this is happening only (more?) for Nikon users.  What is Lightroom doing here?  I'd guess that for the first preview, LR is showing the JPG preview file, which is embedded in the RAW file. Then after a moment, LR renders the RAW file itself to show it's own interpretation.  But why is this interpretation so different from the embedded JPG? Problem with >> inside of \tt I have an inline code example with a nested Java generic declaration, using the typewriter typeface. However, the closing &gt;&gt; is rendering as a black box. A cursory Google search suggested $&gt;&gt;$, but this removes the typewriter font. Using \textgreater in place of the actual &gt; also encounters the same problem. Here is the offending snippet:  ...declaration {\tt List&lt;Map&lt;Integer, String&gt;&gt;} is...   Any ideas?