I have a few of the problems like the one below to solve this week for homework. If someone could give me some help on this one, it would greatly help in getting me started on knowing how to solve the rest of them. Thanks for any help in advance. Love this site.     When throwing a softball directly upward from a height of $5$ ft with an initial velocity of $50$ ft/sec, the height of the softball after $t$ seconds is given by $h(t) = -16t^2+50t+5$ (until the ball hits the ground).   A) Using the limit definition of the derivative, find the velocity $h'(t)$.  B) When is $h'(t) &gt; 0$ and when is $h'(t) &lt; 0$?
A skydiver jumps out of a plane from a height of $2200$m. The skydiver's height, $h$ meters above the ground, can be modeled by the function $$s = 2200 - 4.9t^2$$ How fast is the skydiver falling at $t = 4$s?  If the skydiver is approaching a height of $2200$m, I reasoned that I could use the following definition to find the solution $${f(x+h)-f(x)\over h}$$ I entered the function into this definition and got stuck when I got to this$$f'(x) = \lim_{x\to 0} {2200-4.9t^2-9.8th-4.9h^2\over h}$$ Where can I go from here? Can I continue with this method or did I make a mistake a few steps back? New Solution  How does this look?
How do you empty the buffers and cache on a Linux system? Prior to doing some benchmarking work how would one free up the memory (RAM) that the Linux Kernel is consuming for its buffers and cache?    Note that this is mostly useful for benchmarking. Emptying the buffers and cache reduces performance! If you're here because you thought that freeing buffers and cache was a positive thing, go and read . The short story: free memory is unused memory is wasted memory. How to evaluate environment variables into a string in Python? Low Quality Posts you Have Already Flagged I just discovered that it is possible to get a post in the Low Quality Posts review queue that you have already flagged for closing, making reviewing that item impossible. Obviously, I don't want to 'Looks Good' something that I know should be closed, but at the same time I cannot 'Recommend Close' something I have already flagged leaving the only option being to skip the post.  Can the queue be changed so that it does not show posts which you have already flagged? do_shortcode() within Admin Page I'm using a few plugins that have shortcodes ... however, instead of creating a public page for the content, I've created some new pages within the admin using add_menu_page and I need to know how to utilize do_shortcode() within this context.  As it stands, all the function does it spit out the string. I'm assuming it's because the shortcode API isn't available within an admin page.  How do I get around this? There is no documentation that I can find that explains how to utilize shortcodes within the WP Admin... or if it's even possible.    Specifically I'm trying to utilize WooCommerce shortcodes within the WP Admin. I hate the fact that plugins don't utilize the WP Backend for account/user management. If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English? I've been looking at the python code loging of Blender. But in there things get loged as mouse clicks.  What i like to do is combine a few images into a larger one using compositor, but i need control over compositor by python script. The problem seams to me that it is a bit hard to "spawn" a few nodes, set their values and connect them.  I need an micture of:  image, scale, source image location, mix nodes, output nodes  I have no Code samples other then the log of blender python which in this case is of no big help. Should I load an entire html page with AJAX? Quoting in ssh $host $FOO and ssh $host "sudo su user -c $FOO" type constructs I often end up issuing complex commands over ssh; these commands involve piping to awk or perl one-lines, and as a result contain single quotes and $'s.  I have neither been able to figure out a hard and fast rule to do the quoting properly, nor found a good reference for it.  For instance, consider the following:  # what I'd run locally: CMD='pgrep -fl java | grep -i datanode | awk '{print $1}' # this works with ssh $host "$CMD": CMD='pgrep -fl java | grep -i datanode | awk '"'"'{print $1}'"'"   (Note the extra quotes in the awk statement.)  But how do I get this to work with, e.g. ssh $host "sudo su user -c '$CMD'"?  Is there a general recipe for managing quotes in such scenarios?.. DNS Resolution for example.com - Can you explain? Why are the objects in my hair particle system not sitting on top of the ground? I made a hair particle system and set the Dupli Group to a group of 3 objects. Each of the 3 objects has:   it's origin set to be touching the XY plane (on layer 2) it's Scale applied to 1 and it's Rotation applied to 0     I am trying to get each of the objects to sit directly on top of the ground, but instead, they are centered in the plane, half above the plane and half below the plane:      What am I doing wrong? Here is . The Degree of Zero Polynomial. I wonder why the degree of the zero polynomial is $-\infty$ ?  I heard that, it is $-\infty$ to make the formula $\deg(fg)=\deg(f)+\deg(g)$ hold when one of these polynomials is zero. However, if that was the only reason we could have said that it is $\infty$ instead. Edit Mode buttons for selecting vertices and edges vanished When I am in Edit Mode for my project, the Mesh Select Mode buttons have disappeared!  I loaded the default project and the buttons are where they are supposed to be; the issue is only in my project. Java: Cannot find symbol? How to install the latest Arduino IDE? Load R package from character string Tony's suit is an engineering marvel, and they explain many facets of the technology to help give legitimacy to the special powers, abilities and weapons it has.  I never read the Iron Man comics, but in the movie they really don't have a technological explanation for how he miraculously seems to be unaffected by crushing G-forces of sudden acceleration, the inertia of sudden stops and hair-pin turns, and especially the blunt force trauma from getting smashed in the face with Thor's hammer.  Certainly it appears the suit takes punishment, but Tony always remains unscatched, never a collapsed lung, broken bone or even a bloody nose.  In my infantile understanding of theoretical physics, the same technology that would be used to counter G-forces and sudden blunt force trauma to the body inside would be the very same technology used for  which in my honest opinion would be a much more stunning technological achievement than his heralded Arc Reactor.  Was their ever an explanation proferred for this and if so was it indeed attributed to Anti-Gravity? I am having some issues with the hyperref package. I would like to create a Introduction chapter without a number so I use \chapter*{Introduction} and \addcontentsline{toc}{chapter}{Introduction} because I want it in the table of contents (see example).  But then the link in my PDF viewer gets it wrong and also the automatically created header is no longer correct (see picture). The table of contents shows the right page number (p.1) but the link is also wrong.   What is my mistake here?  \documentclass{scrbook}  \usepackage{hyperref} \usepackage{blindtext} \usepackage{glossaries}   \makeglossaries  \newacronym{eg}{e.g.}{% for example }   \begin{document}   \frontmatter  % abstract before the table of contents \chapter*{Abstract} \addcontentsline{toc}{chapter}{Abstract} \blindtext  \tableofcontents  % chapter with acronyms \cleardoublepage \phantomsection  \printglossary[type=\acronymtype] \addcontentsline{toc}{chapter}{Glossary}  \cleardoublepage \mainmatter   \phantomsection % \chapter{Introduction} % with this everything is correct but I don't want the number \chapter*{Introduction} \addcontentsline{toc}{chapter}{Introduction}  \blindtext  \pagebreak  \blindtext  % first chapter \chapter{Chapter1}  \gls{eg} \blindtext  \pagebreak  \blindtext   \end{document} Rendered image looks pixelated When I hit F12 to render an image and zoom in it is quickly pixelated. How can I render a higher res display? I have looked through the settings and couldn't find a solution. Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$ Let $(v_n)_{n \geq 1} \in \ell ^2$ be a fixed bounded sequence of real numbers. Define a mapping $T$ on $\ell ^{\infty}$ using the formula $$T(a_1, a_2,...)=(v_1a_1,v_2a_2,...), \, \, \, \, \, x=(a_1,a_2,...) \in \ell^{\infty}$$  We can use the fact that, $Tx \in \ell^2 $ for every $x \in \ell^{\infty}$ and $T: (\ell^{\infty},||\cdot ||_{\infty}) \rightarrow (\ell^{2},||\cdot ||_{2})$ is a linear operator.  Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$ for all $x \in \ell^{\infty}$    Here is what I tried:  $||Tx||_2 = \bigg( \sum v_k^2 a_k^2 \bigg)^{1/2} \leq (||x||_{\infty}^2 \sum v_k^2 )^{1/2}= (||x||_{\infty}^2 ||(v_k)||_2^2 )^{1/2} = ||(v_k)||_2 \cdot ||x||_{\infty}$  Is this OK? I was wondering why I couldn't delete my own question. Well actually, I have accepted the question itself to be wrong and even I feel that I have accepted a wrong answer, but when I try to delete my question, I get a message saying that,"This question can't be deleted, flag it for moderator attention". Why is this happening and how can I solve this?