tag:blogger.com,1999:blog-140857722017-06-21T22:45:51.386-05:00Calculus 45SAn interactive learning ecology for students and parents in my Calculus 45S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.comBlogger48125tag:blogger.com,1999:blog-14085772.post-1156884695337416252006-06-29T15:51:00.000-05:002006-09-01T14:02:24.446-05:00The Adventure Continues ...Our adventures in blogging continue....<br /><br />Watch for 3 new blogs going live September 6, 2006 ...<br /><br /><blockquote><ul><li><a href="http://pc30sf06.blogspot.com">Pre-Cal 30S (Fall '06)</a> (Grade 11)</li><li><a href="http://pc40sf06.blogspot.com">Pre-Cal 40S (Fall '06)</a> (Grade 12)</li><li><a href="http://apcalc06.blogspot.com">AP Calculus AB 2006-07</a> (Grade 12)</li></ul></blockquote>Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1151537097286748142006-06-28T18:24:00.000-05:002006-06-28T18:24:57.310-05:00So Long ...<img src="http://static.flickr.com/73/161775713_4ed2bb3663_m_d.jpg" align="right" hspace="8">We had our graduation exercises today. A gentle push into the world for you. I hope you're leaving with the keys to your future in your hand.<br /><br /><b><i>I'm so glad we've had this time together,<br /><br />Just to have a laugh or learn some math,<br /><br />Seems we've just got started and before you know it,<br /><br />Comes the time we have to say, "So Long!"</b></i><br /><br />So long everybody! Watch this space in the fall for pointers to new blogs for each of my classes. <br /><br />Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1149899986365637622006-06-09T19:36:00.000-05:002006-06-09T19:39:46.376-05:00The end or the beginning?<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6469/460/1600/endings%20and%20beginnings%20poster.0.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://photos1.blogger.com/blogger/6469/460/320/endings%20and%20beginnings%20poster.0.jpg" alt="" border="0" /></a><br /><div style="text-align: center;"> As the school year comes to a close, do you view it as an end or a beginning ?<br /></div>Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1148497074102005562006-05-24T13:55:00.000-05:002006-05-24T13:57:54.126-05:00Critical Values<a href="http://photos1.blogger.com/blogger/8171/2241/1600/jjj.jpg"><img style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 436px; CURSOR: hand; HEIGHT: 374px; TEXT-ALIGN: center" height="374" alt="" src="http://photos1.blogger.com/blogger/8171/2241/400/jjj.jpg" width="400" border="0" /></a>Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com1tag:blogger.com,1999:blog-14085772.post-1148484359962956252006-05-24T09:52:00.000-05:002006-05-24T13:18:11.316-05:00Optimization Skill BuildingHere are two games I'd like you to spend some time playing to build your spatial visualization skills:<br /><br /><blockquote><ul><li><a href="http://home.earthlink.net/%7Ecmalumphy/3d.html">3D Tic Tac Toe</a></li><br /><li><a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=125">Can You Build It? Yes You Can!</a><br />(Click on the [+] next to the word <b>Explorations</b>. Use the tools to build the illustrated solid.)</li></ul></blockquote><br /><br />Also spend some time refamiliarizing yourself with the properties and formulas for various geomteric shapes and solids.<br /><br /><blockquote><ul><li><a href="http://www.mathsnet.net/shape/index.html">An Interactive Course on Shapes</a></li><br /><li><a href="http://www.mathsnet.net/geometry/solid/index.html">Interactive Solid Geometry</a><br /></li></ul></blockquote><br /><br />Finally, some reviews and quizzes on solving optimization problems.<br /><br /><blockquote><ul><li><a href="http://www.analyzemath.com/calculus/Problems/First_second_derivative.html">Max and Min of a Function Problems Tutorial</a></li><br /><li><a href="http://www.analyzemath.com/calculus/Problems/optimize_time.html">Distance-time Optimization Problems Tutorial</a></li><br /><li><a href="http://www.analyzemath.com/calculus/Problems/optimize_area.html">Area Optimization Problems Tutorial</a></li><br /><li><a href="http://www.analyzemath.com/calculus/Problems/derivative_graph.html">Using Derivatives to Graph Functions Tutorial</a></li><br /><li><a href="http://www.funtrivia.com/playquiz/quiz1899122fb10.html">Problem Solving Quiz<br />(Do only questions 1-3.)</a></li><br /><li><a href="http://www2.scc-fl.edu/lvosbury/CalculusI_Folder/OptimizationProblems.htm">Optimization Problems with Solutions and Animations<br />(The animations are great! They'll really help you to understand what's going on.)</a></li></ul></blockquote><br /><br />Email me if you hit any snags. ;-)<br /><br />Cheers!<br />Mr. K.Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1147828126079892822006-05-16T20:07:00.000-05:002006-05-17T09:16:15.073-05:00Maxima and Minima<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/8171/2241/1600/Picture.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://photos1.blogger.com/blogger/8171/2241/400/Picture.jpg" alt="" border="0" /></a><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/8171/2241/1600/quiz%20page%201.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://photos1.blogger.com/blogger/8171/2241/400/quiz%20page%201.jpg" alt="" border="0" /></a><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/8171/2241/1600/quiz%20page%202.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://photos1.blogger.com/blogger/8171/2241/400/quiz%20page%202.jpg" alt="" border="0" /></a>Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com1tag:blogger.com,1999:blog-14085772.post-1147569538013672732006-05-13T20:11:00.000-05:002006-05-13T20:21:23.520-05:00Starting Over--<small><span style="font-family:comic sans ms;">It's been pretty quiet on this blog. I'm afraid that perhaps in my enthusiasm to join your blog and learn what I could of calculus, I burst into your space instead of entering unobtrusively. Maybe the best analogy is that I was too much like a young kid running into a room excited to share what was going on. I never introduced myself, just started right in. But I'm not a young kid, and a 60 year old woman should know much better! :) I hope you'll let me start over again--<br /><br />Hi! My name is Lani. My former students called me Mrs. Hall or Ms. Ritter. I hope you might feel comfortable using my first name.<br /><br />Who am I: I live in Ohio. I am a former classroom teacher; I taught for 33 years in the United States and two years in Ontario, Canada. (My mother was Canadian and I have many relatives in Ontario.) I design online courses for teachers now, working from home on my computer. I cherish the memories of those 35 years and I keep in touch with many of my students. I love to cook, garden, read and walk with my husband and our German shepherd, Harley, in the park.<br /><br />How did I get here: I learned about your blog from Mr. K . I had emailed him to let him know that I hoped I might become a mentor for some of his students (I miss the interaction with students). Mr. K. agreed that I might become a mentor (even when he learned that I am not strong in math!) and I chose your class!<br /><br />Why am I here: I hoped to learn some calculus AND I wanted an opportunity to engage young people again in conversations about learning and life.<br /><br />Now that I think about it, we do a lot of starting over in school and life don't we? I remember when I was young, before computers, I used to start over a lot so my homework would be just right. Thank goodness computers now make it easier to fix those mistakes! I started over when my family moved when I was in the fifth grade; we left New York for Michigan. I started over when I went away to college in Indiana. I started over when I moved to Ontario to teach for two years. I start over a lot when I write, trying to get just the right word that captures what I mean. I start over often when I speak, for the same reason. My list could go on and on. Do you think you'll have a long list too, by the time you get to 60? I wonder if this whole notion of starting over, has to do with learning all our lives?. Do you think?<br /><br />And so I start over again here, hoping that you'll share some of what you are learning with me. If you're willing, can you explain some of the basic calculus concepts you've learned with me and also what you know of starting over?<br /></span></small>Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1146095513440104612006-04-26T18:50:00.000-05:002006-04-26T18:53:09.613-05:00Perseverance<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6469/460/1600/perseverance.jpg"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer;" src="http://photos1.blogger.com/blogger/6469/460/200/perseverance.jpg" alt="" border="0" /></a><br />Would you agree? Have you had lots of perseverance lately?Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1145824937524605042006-04-23T15:42:00.000-05:002006-04-23T15:58:41.066-05:00The DaVinci Code Quest Sunday<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6380/769/1600/codequest.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://photos1.blogger.com/blogger/6380/769/320/codequest.jpg" alt="" border="0" /></a><br /><br />It started last week. Google releases one puzzle each day for 24 days until the movie "The Da Vinci Code" is released in May. So far 7 puzzles have been released. You have to solve the puzzle to reveal a clue. Then you have to answer the clue question(s) to advance to the next puzzle. You can win a prize for solving all 24 puzzles. Now I realize this is all about marketing and they're really just trying to get as many of us as possible to go see the movie but the puzzles are really cool! Google searching often helps to find the answers. One of the puzzle questions can be answered using <a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut55_count.htm">The Fundamental Principle of Counting</a> and the very first (sudoku-like) puzzle uses a couple of mathematical symbols.<br /><br /><b><u>Challenge 1:</u></b> What is the question that can be solved using The Fundamental Principle of Counting and how do you use the counting principle to find the answer?<br /><br /><b><u>Challenge 2:</u></b> What mathematical symbol is used in the very first puzzle and what number does it represent? (Not the "delta," in a later puzzle it has a different meaning.)<br /><br />You have to <a href="e=http://www.google.com/ig/setp%3Furl%3Dhttp://www.google.com/ig/setp%253Fet%253D_jjWaRwQ5iQ%2526url%253Dhttp://www.google.com/ig/game%25253Faction%25253Dinstall%252526l%25253DUS%252526game%25253Ddavinci%252526et%25253D_jjWaRwQ5iQ%252526tos%25253D1%2526n_37%253D&followup=http://www.google.com/ig/setp%3Furl%3Dhttp://www.google.com/ig/setp%253Fet%253D_jjWaRwQ5iQ%2526url%253Dhttp://www.google.com/ig/game%25253Faction%25253Dinstall%252526l%25253DUS%252526game%25253Ddavinci%252526et%25253D_jjWaRwQ5iQ%252526tos%25253D1%2526n_37%253D">sign up for a Google Homepage</a> in order to play, but that's a free and very useful service. After that you can <a href="http://flash.sonypictures.com/movies/davincicodequest/">begin the game</a>. Click on the US button to start 24 days of fun! (Actually, 17 because you could work through the first eight today.) Don't forget to also find the answers to the <b>Challenge Questions</b> above!. ;-)Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1145408050574544072006-04-18T19:11:00.000-05:002006-04-18T19:54:11.363-05:00Higher Order Derivatives<a href="http://photos1.blogger.com/blogger/8171/2241/1600/today.jpg"><img style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/today.jpg" border="0" /></a>Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1144971105078751462006-04-13T18:31:00.000-05:002006-04-13T18:33:35.873-05:00doing-- understanding---<span style="font-family:Arial;">Thank you so much for sharing what you are learning. I’ve been carefully reading your scribes trying to learn along with you, knowing that I’d probably understand better if I was on the “doing” end as you are when you are scribing. I remember this old saying:</span><br /><span style="font-family:Arial;"></span><br /><span style="font-family:Arial;">What I hear, I forget.<br />What I see, I remember.<br />What I do, I understand. - <span style="font-style: italic;">Kung Fu Tzu (Confucius)</span></span><br /><span style="font-family:Arial;"></span><br /><span style="font-family:Arial;">I’ve found this is very true for me, especially when I am learning something new on the computer, trying to understand how a teaching strategy might work, or teaching myself a new recipe.</span><br /><span style="font-family:Arial;"></span><br /><span style="font-family:Arial;">I wondered--- have you found this is true for you also? How do you find your scribes help you understand all that you learn in calculus? Does “doing” help you understand in your other courses too? Or may be not?</span><br /><span style="font-family:Arial;"></span><br /><span style="font-family:Arial;">Best,</span><br /><span style="font-family:Arial;">Lani</span>Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1144809780986568292006-04-11T20:59:00.000-05:002006-04-11T21:43:01.330-05:00The derivative of a constant times a function and the derivative of a power function<img style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 444px; CURSOR: hand; HEIGHT: 390px; TEXT-ALIGN: center" height="106" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/april.jpg" width="138" border="0" />The derivative of a power function<br /><br /><img style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/a.jpg" border="0" />Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1144609565278802052006-04-09T14:05:00.000-05:002006-04-09T14:08:33.320-05:00Four Colour Sunday!<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6380/769/1600/fourcolour.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/6380/769/400/fourcolour.jpg" border="0" alt="" /></a><br />You may have <a href="http://en.wikipedia.org/wiki/Four_color_theorem">heard</a> that any map can be coloured with four colours in such a way that neighbouring countries receive different colours. That it can be always done is one thing. How to do it is another. Are you ready to <a href="http://www.puzzle.jp/four_color_problem-e.html">start colouring</a>?<br /><br />(<i>Thanks again to <a href="http://simpler-solutions.net/pmachinefree/thinkagain/thinkagain.php">Think Again!</a></i>)Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1144275063057539652006-04-05T16:32:00.000-05:002006-04-05T17:17:54.230-05:00Scribe! The Chain Rule, and songHi this is Van, and doing the weekly scribe. So, let's get this started. Yay!, no pictures to put in or make!, I love my job, anyways onto the scribe.<br /><br /><br /><br />So, we started the class off with our 4 question, multiple choice quiz. 8 minutes long. Then we did practice questions. Which were:<br /><br />a f(x) = <u>4</u>x³- <u>1</u>x²+5x - 7<br /><br />b g(x) = (2x² - 1) ( x³ - 4x + 3)<br /><br />c h(x) = <u>2x - 3</u><br /> x² - 4<br /><br />This is our first class after spring break, so I completely forgot about the Product rule and Quotient rule. So Mr. K teaches us a song that helps us remember them both. Here it goes.<br /><br />The quotient rule you wish to know is lowdy high minus highdy low.<br />Put a line and down below<br />Denominator squared will go<br />The product rule you have in rhyme<br />Is one prime two plus one two prime<br /><br />You sing it in a way, that makes it sound like twinkle twinkle little star.<br /><br />So after the questions we are given a question that looks like this<br /><br /><sqr>x²-3x</sqr><br /><br />We've never dealt with a problem like this before. So, we apply Function DeComposition and it looks like this.<br /><br />f(x) = <sqr>x</sqr><br />g(x) = x²-3x<br /><br />We are then given a rule. For situations like this. It's called the <span style="font-weight: bold;">Chain Rule</span>. And the chain rule says this:<br /><br />F(x) = f(g(x))<br />F'(x) = f'(g(x)) - g'(x)<br /><br />So we implement this new found rule onto our question.<br /><br />F(x) = <sqr>x² - 3x</sqr><br /> = (x²-3x)^½<br /><br />f(x) = x^½<br />g(x) = x² - 3x<br />f'(x) = ½ x^½<br />g'(x) = 2x - 3<br /><br />F'(x) = ½(x² - 3x)^-½ ٠ 2x - 3<br /><br /><br />So, after we went through our first example, we did another one<br /><br />h(x) = (x³ - 3x)²<br />h(x) = f(g(x))<br />h'(x) = 2(x³ - 3x)(3x²-3)<br /> = 2[3x^5 - 12x³ + 9x<br /> = 6x^5 - 24x³ + 18x<br /><br />That was using our chain rule. Here's if we do it manually without the chain rule.<br /><br />h(x) = (x³ - 3x)(x³ - 3x)<br /> = x^6 - 6x^4 + 9x²<br />h'(x) = 6x^5 - 24x³ + 18x<br /><br />It may look easier, but Mr. K says, use the chain rule. It will be much more efficient when you advance further into Calculus.<br /><br />Homework in the white and orange book is... all questions up to and including Page 77 and in the blue book is page 20.<br /><br />Thank you, and next scribe can only be one other person... Temesgen. (2 person class, wee)<br /><br />once again, I don't know how to place square roots over things. AnnoyingVanhttp://www.blogger.com/profile/16521408733815276486noreply@blogger.com3tag:blogger.com,1999:blog-14085772.post-1144206785011753252006-04-04T22:10:00.000-05:002006-04-04T22:13:05.023-05:00derivative of a quotient rule and derivative of a product rule<a href="http://photos1.blogger.com/blogger/8171/2241/1600/untitled.2.jpg"><img style="FLOAT: left; MARGIN: 0px 10px 10px 0px; CURSOR: hand" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/untitled.2.jpg" border="0" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><a href="http://photos1.blogger.com/blogger/8171/2241/1600/untitled1.0.jpg"><img style="FLOAT: left; MARGIN: 0px 10px 10px 0px; CURSOR: hand" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/untitled1.0.jpg" border="0" /></a>Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1144007019007312982006-04-02T14:43:00.000-05:002006-04-02T14:43:39.020-05:00Roboclaw Sunday!<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6380/769/1600/roboclaw.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/6380/769/200/roboclaw.jpg" border="0" alt="" /></a><br />Move the robot arm to pick up the ball. Clean, simple design. I got to level 19. I died. <a href="http://www.scenta.co.uk/minisites/flash/roboclaw/index.html">It's a doozy!</a>Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1143992561684525612006-04-02T10:41:00.000-05:002006-04-02T10:44:16.973-05:00Scribing once a week? Possibilities?<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/6469/460/1600/mypossibilitiesposter.jpg"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/6469/460/200/mypossibilitiesposter.jpg" border="0" alt="" /></a><br /><span style="font-size:85%;"><span style="font-family:comic sans MS;">Van noted scribing once a week is a lot of work. Yes it is! How might an “idealist” confront the possibilities of those scribes?</span></span>Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1143302339747713282006-03-25T09:58:00.000-06:002006-03-25T09:58:59.873-06:00A del.icio.us idea ...We talked about this in class on Thursday. Students often find more, and better, sites than I do. You're better websurfers than I am. ;-) That got me thinking .....<br /><br />I spend a <b>lot</b> of time looking for good websites that help us learn in this class. But what if we all spent a <b>little</b> time doing that? What if there was an easy way for us to both save our bookmarks (without cluttering up our <b>favourites</b> list) and share them with the whole class with the click of a single button? And what if we could access those bookmarks not just from home, but from any computer in the world? Hmmm .....<br /><br />Well, there is an easy way to do that! Instead of saving bookmarks on your home computer sign up for a free account at a site called <a href="http://del.icio.us">del.icio.us</a>. You can then access them from any computer in the world. You can easily install a little button/bookmark that allows you to save any webpage you're looking at without interupting your surfing. Now we can all make recommendations to each other learning resources with the click of a single button in our <a href="http://del.icio.us">del.icio.us</a> accounts! Tag it using this tag:<br /><br />cal45s<br /><br />You should also tag each entry with several other words that indicate what it is about; things like: trig graphing stats circles etc. Also, include a brief descriptive clipping from the site (or type one in yourself).<br /><br />As soon as someone starts saving links I'll add a <b>del.icio.us box</b> to the bottom of the sidebar of our blog. It will show the 10 most recently saved links <b>automatically</b> as you find them. There is will also be a link to the entire archive that you can browse at your leisure.<br /><br />You can <a href="http://www.beelerspace.com/index.php?p=890">read this</a> tutorial on how to get started with <a href="http://del.icio.us">del.icio.us</a>. You might also be interested in watching <a href="http://weblog.infoworld.com/udell/gems/delicious.html">this screencast</a> that illustrates just how powerful this web tool is.<br /><br />Remember, this is part of your homework for Spring Break. You must save at least two links for each unit we have studied so far. Try not to post a link that someone else has already found. You can see what's already been posted by looking in <a href="http://del.icio.us/tag/cal45s">our archive</a>.Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1143177487300040702006-03-23T22:35:00.000-06:002006-03-23T23:18:07.433-06:00Derivatives of, and Definitions of a derivativeSo, I'll start my scribe now, since it involves no pictures, it should be quick n' easy. Woohoo! Anyways, here I go, Enjoy!<br /><br />I came late to Calculus (oh no!) by 15 minutes (a big oh no!), so I missed the quiz. Alarm didn't go off, mom did. Boy that wasn't fun. Anywho, we wrote in our math dictionaries. The notes looked like this:<br /><br />Derivative of:<br /><br />A constant function<br /><br />f(x) = k f'(x) = lim f(x+h) - f(x)<br /> h->0 h<br /><br />The Derivative of a = lim k-h <br />constant funcion h->0 h<br />is ZERO.<br /> = lim 0<br /> h->0 h<br /><br /> = 0<br /><br />A linear function<br /><br />f(x) = mx+b f'(x) = lim f(x+h) - f(x)<br /> h->0 h<br /><br />The limit of a = lim [m(x+h)+h] - [mx+b]<br />linear function h->0 h<br />is the slope of<br />the line. = lim mx + mh + b - mx - b<br /> h->0<br /><br /> = lim mh<br /> h->0 h<br /><br /> = lim m = m<br /> h->0<br /><br /><br />So, after all those notes, Mr.K said, we are to do something different, but are going to go back to that stuff up there in future classes. He needs to pay attention to these things first he says. So, different notes, but related, are appearing on the board.<br /><br />The Definition Of A Derivative<br /><br />f'(x) = lim f(x+h) - f(x)<br /> h->0 h<br /><br />A derivative is:<br /><br />The slope of a tangent line<br />A rate of change<br /><br /><br />A summary of derivative rules.<br /><br />Constant function : f(x) = k f'(x) = 0<br />Power function : f(x) = x^n f'(x) = nx^(n-1)<br />Constant times a function : f(x) = kg(x) f'(x) = kg'(x)<br />A sum or difference of a function(s) : f(x) = g(x) +/- h(x) f'(x) = g'(x) +/- h'(x)<br /><br />*note the +/- is the + over the - , so we're not dividing here. I couldn't find that character on the character map. Sorry for the incovinience.<br /><br />Ex. Find the derivative of :<br /><br />f(x) = 3x² - 2x + √x - 5<br />f'(x) = 3▪2x - 2 + (1/2)^x^-1/2<br /> = 6x - 2 + 1/2√x<br /><br />*note the √ is square root, and the ^'s are to the power of. Since I've never done a proper scribe, tell me all those commands that give it the oh so nice look.<br /><br />I hope this helps. Next scribe will be Temesgen.<br /><br />But now, there's only 2 of us, Calvin dropped, so, we have to work something out. Scribing once a week is a lot of work!<br /><br />Enjoy!Vanhttp://www.blogger.com/profile/16521408733815276486noreply@blogger.com1tag:blogger.com,1999:blog-14085772.post-1142988454390859262006-03-21T17:12:00.000-06:002006-03-21T19:29:51.100-06:00DerivativeIn todays class we started with a quiz as usual. And Mr.k wrote 4 question on the board which's similar to the question below:<br /><br /><br /><a href="http://photos1.blogger.com/blogger/8171/2241/1600/untitled.jpg"><img style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" height="337" alt="" src="http://photos1.blogger.com/blogger/8171/2241/320/untitled.jpg" width="364" border="0" /></a>And if you were ask to write the equation of the line tangent to f(x) first thing to do:<br /><ul><li>find the slope of the tangent</li><li>(1,y) find the y value by substituting the 1 into the equation</li><li>which in this case is y value = 15</li><li>(1,15) and slope m=8</li><li>Use the y-y=m(x-x) to write the equation<br /></li></ul><p>Page 30-36 was assigned for homework and page 16 in the blue booklet. Next scribe is calvinw. </p>Temesgenhttp://www.blogger.com/profile/12054619691174558325noreply@blogger.com1tag:blogger.com,1999:blog-14085772.post-1142837395710029672006-03-19T21:56:00.000-06:002006-03-20T21:29:12.656-06:00ScribeSorry for the delay in the post. Just been busy for the weekend. This scribe post will be for Thursday, March 16, 2006. So here I go.<br /><br />We started class with a small multiple choice quiz. It consisted of 4 questions and the quiz lasts 8 minutes, and begins at the start of class.<br /><br />So we discussed a tangent line.<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/898/2239/1600/Scribe.2.jpg"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer;" src="http://photos1.blogger.com/blogger/898/2239/320/Scribe.2.jpg" alt="" border="0" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />ex. f(x) = x² @ x=3<br /><br /> f(3) = (3)²<br /><br /> = 9<br /><br /> f(3+h) = (3+h)²<br /><br /> = 9 + 6h + h²<br /><br />d y = lim f(3+h) - f(3)<br />d x h-> 0 h<br /><br /> = lim 9 + 6h + h² - 9<br /> h ->0 h<br /><br /> = lim 6h + h²<br /> h ->0 h<br /><br /> = lim 6+h<br /> h->0<br /><br /> = lim 6<br /> h->0<br /><br />There, revised. That's what I originally wanted it to look like. Sorry if it still doesn't help.<br /><br />Next scribe is TemesgenVanhttp://www.blogger.com/profile/16521408733815276486noreply@blogger.com2tag:blogger.com,1999:blog-14085772.post-1142794454671855102006-03-19T12:54:00.000-06:002006-03-19T12:54:14.680-06:00Box Up Sunday!This is a clever little game. You've got to get the small blue box inside the large red box. You can only push a box from the inside. The black boxes, if used cleverly, can help you get the blue box inside the red one. But sometimes they're just in the way. I made it to level 4 pretty quickly, but then it starts getting tough. How far can you go? ;-)<br /><br /><a href="http://lightforce.freestuff.gr/boxup.php">Have fun with this!</a><br /><br /><center><img src="http://www.archive.org/download/boxup1.jpg_1/boxup1.jpg"></center>Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1142730428088983452006-03-18T19:07:00.000-06:002006-03-18T19:09:22.863-06:00Challenge<div style="float: right; margin-left: 10px; margin-bottom: 10px;"> <a href="http://www.flickr.com/photos/53781974@N00/114384102/" title="photo sharing"><img src="http://static.flickr.com/36/114384102_86e026a1c4_m.jpg" alt="" style="border: 2px solid rgb(0, 0, 0);" /></a><br /><span style="margin-top: 0px;font-size:0;" > <a href="http://www.flickr.com/photos/53781974@N00/114384102/">challenge</a> <br /> Originally uploaded by <a href="http://www.flickr.com/people/53781974@N00/">laniritterhall</a>. </span></div><span style="font-family: comic sans ms;">I'm wondering if this challenge has anything to do with calculus? Can you help me out?</span><br /><br /><span style="font-family: comic sans ms;">Best,</span><br /><span style="font-family: comic sans ms;">Lani</span>Lani Ritter Hallhttp://www.blogger.com/profile/16352862711544966770noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1142405004358914362006-03-15T00:43:00.000-06:002006-03-15T00:44:47.503-06:00The "New" GuyNow I bet you guys have been wondering who this Gerald (M) character is under the contributors list for a while now. While I did mean to introduce myself earlier, now is better than never. I, Gerald (M), am a member of Mr. K's mentorship project, and while I don't claim to have all the answers, you can rest assured that I will try my absolute best you help out any way possible (and hopefully not make things any worse, as I am also just a student).<br /><br /><a style="font-style: italic;" title="Click for further information about this quotation" href="http://www.quotationspage.com/quote/26184.html">"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater."</a><br /><br /><div style="text-align: right;"> - Albert Einstein</div>Gerald (M)http://www.blogger.com/profile/02210826933063845594noreply@blogger.com0tag:blogger.com,1999:blog-14085772.post-1142376139026678502006-03-14T16:37:00.000-06:002006-03-14T16:50:10.836-06:00Seek and ye shal find ....<img src="http://photos3.flickr.com/4024795_9a950a4335_m_d.jpg" align="right" hspace=8><br /><br />The Coin Hunt has officially begun as of 12:30 this afternoon. The race is on! Who will be the first to find the coin? Will the students find their coin before the teachers find theirs? Who will win the pizza party? Which charity will benefit from this year's hunt?<br /><br />Check the walls of the building as you walk into school in the morning for hints to figuring out the puzzles.<br /><br /><b><i>Happy <font size="+2">π</font> Day!!<br />Have fun with it. ;-)</i></b>Darren Kuropatwahttps://plus.google.com/116565501620976083429noreply@blogger.com0