MaplePrimes - Questions and Posts tagged with calculus
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 25 Apr 2014 09:34:27 GMTFri, 25 Apr 2014 09:34:27 GMTThe most recent questions and posts on MaplePrimes tagged with calculushttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with calculus
http://www.mapleprimes.com/tags/calculus
How do I solve a system of equations in Maple 17 for Mac?
http://www.mapleprimes.com/questions/201258-How-Do-I-Solve-A-System-Of-Equations?ref=Feed:MaplePrimes:Tagged With calculus
<p>I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs. I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:</p>
<p>>solve({2*x+3*y=7,5*x+8*y=9},{x,y}); </p>
<p>in order to receive the answer </p>
<p>{y=-17,x=29}.</p>
<p> </p>
<p>Instead, I have received the following error message, which has no help attached to it through the help page.</p>
<p>solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});<br>Warning, solving for expressions other than names or functions is not recommended.</p>
<p>I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution. I would greatly appreciate any guidance!</p><p>I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs. I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:</p>
<p>>solve({2*x+3*y=7,5*x+8*y=9},{x,y}); </p>
<p>in order to receive the answer </p>
<p>{y=-17,x=29}.</p>
<p> </p>
<p>Instead, I have received the following error message, which has no help attached to it through the help page.</p>
<p>solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});<br />Warning, solving for expressions other than names or functions is not recommended.</p>
<p>I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution. I would greatly appreciate any guidance!</p>201258Sat, 29 Mar 2014 14:53:26 ZebetwalshebetwalshHow do I plot this orthogonal trajectories equation?
http://www.mapleprimes.com/questions/201120-How-Do-I-Plot-This-Orthogonal-Trajectories?ref=Feed:MaplePrimes:Tagged With calculus
<p>I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:</p>
<p>dy/dx = (x^2) - (2y^2) - C = 0</p>
<p>This is what I had so far:</p>
<p> </p>
<p>restart;</p>
<p>with(DEtools):</p>
<p>with(plots):</p>
<p> </p>
<p>Function:=unapply(simplify(x^2-2y^2-C),(x,y)):</p>
<p>'Function'(x,y) = Function(x,y);</p>
<p>plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):</p>
<p>plot1:=display(seq(plotFunction(a),a=-5..5)):</p>
<p>display(plot1);</p>
<p> </p>
<p>This is only display one family. How do I code for it plot the other families?</p>
<p>(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)</p>
<p>Please help.</p><p>I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:</p>
<p>dy/dx = (x^2) - (2y^2) - C = 0</p>
<p>This is what I had so far:</p>
<p> </p>
<p>restart;</p>
<p>with(DEtools):</p>
<p>with(plots):</p>
<p> </p>
<p>Function:=unapply(simplify(x^2-2y^2-C),(x,y)):</p>
<p>'Function'(x,y) = Function(x,y);</p>
<p>plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):</p>
<p>plot1:=display(seq(plotFunction(a),a=-5..5)):</p>
<p>display(plot1);</p>
<p> </p>
<p>This is only display one family. How do I code for it plot the other families?</p>
<p>(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)</p>
<p>Please help.</p>201120Wed, 12 Mar 2014 16:50:22 Ztrja4528trja4528Multivariate Taylor expansion
http://www.mapleprimes.com/questions/200347-Multivariate-Taylor-Expansion?ref=Feed:MaplePrimes:Tagged With calculus
<p>How can I expand the mutivariate taylor series of the functions below about the point (x,y)</p>
<p><strong>f(h*a[2]+x, h*a[2]*k[1]+y);</strong></p>
<p><strong> and </strong></p>
<p><strong>f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);</strong></p><p>How can I expand the mutivariate taylor series of the functions below about the point (x,y)</p>
<p><strong>f(h*a[2]+x, h*a[2]*k[1]+y);</strong></p>
<p><strong> and </strong></p>
<p><strong>f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);</strong></p>200347Fri, 29 Nov 2013 20:54:54 ZabbeykabirabbeykabirMaple 17 Won't plot this
http://www.mapleprimes.com/questions/200186-Maple-17-Wont-Plot-This-?ref=Feed:MaplePrimes:Tagged With calculus
<p>I copied and pasted this from the example page and I have to get this same graph for an assignment</p>
<p>im using maple 17</p>
<p> </p>
<p><img src="http://www.maplesoft.com/support/help/helpview.aspx?si=6121/file05121/math296.png" alt="Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)" width="424" height="27"></p>
<p> </p>
<p>when i hit enter the return was</p>
<p> </p>
<p><br><img src="http://www.maplesoft.com/support/help/helpview.aspx?si=6121/file05121/math296.png" alt="Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)" width="424" height="27"> <strong>(1)</strong></p>
<p> </p><p>I copied and pasted this from the example page and I have to get this same graph for an assignment</p>
<p>im using maple 17</p>
<p> </p>
<p><img src="http://www.maplesoft.com/support/help/helpview.aspx?si=6121/file05121/math296.png" alt="Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)" width="424" height="27"></p>
<p> </p>
<p>when i hit enter the return was</p>
<p> </p>
<p><br><img src="http://www.maplesoft.com/support/help/helpview.aspx?si=6121/file05121/math296.png" alt="Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)" width="424" height="27"> <strong>(1)</strong></p>
<p> </p>200186Mon, 11 Nov 2013 23:18:40 ZAcoustikid11Acoustikid11Max/Min Problems in Maple 17
http://www.mapleprimes.com/questions/200036-MaxMin-Problems-In-Maple-17?ref=Feed:MaplePrimes:Tagged With calculus
<p>Hello All,</p>
<p>I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.</p>
<p> </p>
<ol>
<li>In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.</li>
</ol>
<p> a. What do we know about the gradients of F and the ellipse at those points?</p>
<p> b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+ (y-4)^2=1.</p>
<p> </p>
<p> 2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are $7 for x, $12 for y, and $18 for z.</p>
<p> a. Create the cost function</p>
<p> b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.</p>
<p>Any help you could give me would be much appreciated. Thanks!!</p>
<p> </p>
<p> </p>
<p> </p><p>Hello All,</p>
<p>I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.</p>
<p> </p>
<ol>
<li>In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.</li>
</ol>
<p> a. What do we know about the gradients of F and the ellipse at those points?</p>
<p> b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+ (y-4)^2=1.</p>
<p> </p>
<p> 2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are $7 for x, $12 for y, and $18 for z.</p>
<p> a. Create the cost function</p>
<p> b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.</p>
<p>Any help you could give me would be much appreciated. Thanks!!</p>
<p> </p>
<p> </p>
<p> </p>200036Sun, 27 Oct 2013 22:27:54 ZmclifftonmclifftonHow to get CriticalPoints to return only valid critical points
http://www.mapleprimes.com/questions/200025-How-To-Get-CriticalPoints-To-Return?ref=Feed:MaplePrimes:Tagged With calculus
<p>I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).</p>
<p> </p>
<form name="worksheet_form">
<table style="width: 768px;" align="center">
<tbody>
<tr>
<td>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/9a849500d0e29c1b8264b2b88f905e7e.gif" alt="with(Student[Calculus1]):" width="174" height="23"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/08808f16ffa42516811c95a44e6405a1.gif" alt="f := proc (x) options operator, arrow; x^2*ln(x) end proc:" width="120" height="27"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/a80156cd34f5a88b37175f7c5cfc6069.gif" alt="`assuming`([CriticalPoints(f(x))], [x > 0])" width="228" height="23"></p>
<table>
<tbody>
<tr valign="baseline">
<td>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/e6c7f2af51c223973c557d348fe58ad8.gif" alt="[0, exp(-1/2)]" width="61" height="42"></p>
</td>
<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td>
</tr>
</tbody>
</table>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/1944657402be5a35fccc1a77149af928.gif" alt="``" width="11" height="23"></p>
</td>
</tr>
</tbody>
</table>
<input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form>
<p>My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)? As seen above, my attempt to use the assuming command proved futile.</p>
<p>More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?</p>
<p> </p>
<p><a href="/view.aspx?sf=200025_question/critpts.mw">Download critpts.mw</a></p><p>I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).</p>
<p> </p>
<form name="worksheet_form">
<table style="width: 768px;" align="center">
<tbody>
<tr>
<td>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/9a849500d0e29c1b8264b2b88f905e7e.gif" alt="with(Student[Calculus1]):" width="174" height="23"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/08808f16ffa42516811c95a44e6405a1.gif" alt="f := proc (x) options operator, arrow; x^2*ln(x) end proc:" width="120" height="27"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/a80156cd34f5a88b37175f7c5cfc6069.gif" alt="`assuming`([CriticalPoints(f(x))], [x > 0])" width="228" height="23"></p>
<table>
<tbody>
<tr valign="baseline">
<td>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/e6c7f2af51c223973c557d348fe58ad8.gif" alt="[0, exp(-1/2)]" width="61" height="42"></p>
</td>
<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td>
</tr>
</tbody>
</table>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=200025_question/1944657402be5a35fccc1a77149af928.gif" alt="``" width="11" height="23"></p>
</td>
</tr>
</tbody>
</table>
<input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form>
<p>My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)? As seen above, my attempt to use the assuming command proved futile.</p>
<p>More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?</p>
<p> </p>
<p><a href="/view.aspx?sf=200025_question/critpts.mw">Download critpts.mw</a></p>200025Sat, 26 Oct 2013 23:04:06 ZDJJerome1976DJJerome1976Sequence of real numbers
http://www.mapleprimes.com/questions/152015-Sequence-Of-Real-Numbers?ref=Feed:MaplePrimes:Tagged With calculus
<p>A sequence of real numbers <img class="latex" style="vertical-align: -3px;" src="http://data.artofproblemsolving.com/images/latex/e/7/4/e74b2dca14e7be4b1bdd9de6302fa509fc781bcd.gif" alt="a_1,a_2,a_3......."> satisfies <img class="latex" style="vertical-align: -2px;" src="http://data.artofproblemsolving.com/images/latex/1/a/0/1a03c2c5b97ca17ee64f09758aab5498d248d620.gif" alt="a_0=1"> and<br><br><p>A sequence of real numbers <img class="latex" style="vertical-align: -3px;" src="http://data.artofproblemsolving.com/images/latex/e/7/4/e74b2dca14e7be4b1bdd9de6302fa509fc781bcd.gif" alt="a_1,a_2,a_3......."> satisfies <img class="latex" style="vertical-align: -2px;" src="http://data.artofproblemsolving.com/images/latex/1/a/0/1a03c2c5b97ca17ee64f09758aab5498d248d620.gif" alt="a_0=1"> and<br><br><img class="latex" style="vertical-align: -3px;" src="http://data.artofproblemsolving.com/images/latex/1/6/5/165bcaa18361391da0a3a25d85cfeb7b7defdcf5.gif" alt="a_{n+1}=2016a_{n} +a_{n-1}-1"> , Evaluate <img class="latex" style="vertical-align: -2px;" src="http://data.artofproblemsolving.com/images/latex/4/8/3/4833aa063f1240c2498d479836a95e989740e987.gif" alt="a_{2016}">?</p>152015Sat, 21 Sep 2013 18:59:51 ZyangthearyyangthearyHow to make a table of multivariable equation variable values?
http://www.mapleprimes.com/questions/151516-How-To-Make-A-Table-Of-Multivariable?ref=Feed:MaplePrimes:Tagged With calculus
<p>How would one go about making a table of variable values for a multivariable equation? By that I mean, lets say you have the equation x-3y+z=5. It can easily be plotted as a plane but what if I wanted to produce a list of key values so I could make a graph myself? Similar to how the TI's can make a table for single variable equations. I ask because I am tasked with making a pencil and paper graph and it would be nice if I had a table that were say, incremented by x=1. Is there...<p>How would one go about making a table of variable values for a multivariable equation? By that I mean, lets say you have the equation x-3y+z=5. It can easily be plotted as a plane but what if I wanted to produce a list of key values so I could make a graph myself? Similar to how the TI's can make a table for single variable equations. I ask because I am tasked with making a pencil and paper graph and it would be nice if I had a table that were say, incremented by x=1. Is there any such way? It gets very tricky with multiple variables.</p>151516Mon, 09 Sep 2013 04:35:51 ZwestonforbeswestonforbesGet area under curve from spreadsheet data
http://www.mapleprimes.com/questions/150395-Get-Area-Under-Curve-From-Spreadsheet-Data?ref=Feed:MaplePrimes:Tagged With calculus
If I have spreadsheet data, x and y (velocity and time), I need to find distance. I see numbers of ways to do this, however, I wonder what people would suggest as the fastest / easiest way. I'm not needing a function really, just results. Does Maple have tools to simplyify this process, and if not, what process(s) might yield results of determinable or selectable accuracy. I will have many sets of data in the future that need to be manipulated...If I have spreadsheet data, x and y (velocity and time), I need to find distance. I see numbers of ways to do this, however, I wonder what people would suggest as the fastest / easiest way. I'm not needing a function really, just results. Does Maple have tools to simplyify this process, and if not, what process(s) might yield results of determinable or selectable accuracy. I will have many sets of data in the future that need to be manipulated in this way. It would also be in the future, helpful, to have functions. The curve fitting assistant produces piecewise functions for the curve I am currently observing.150395Mon, 12 Aug 2013 18:12:53 ZDavidRussoDavidRussousing region fill in approximate integration
http://www.mapleprimes.com/questions/150094-Using-Region-Fill-In-Approximate-Integration?ref=Feed:MaplePrimes:Tagged With calculus
<p>The Single Variable Calculus Approximate Integration Tutor (and the function ApproximateInt) work fine for the built-in example of sin(x) from 0 to Pi. But if you change it to sin(Pi*x) from 0 to 1 then plot options are ignored. And if you ask to integrate sin(3.1415926*x) from 0 to 1, then it works again. Is there a work-around?</p><p>The Single Variable Calculus Approximate Integration Tutor (and the function ApproximateInt) work fine for the built-in example of sin(x) from 0 to Pi. But if you change it to sin(Pi*x) from 0 to 1 then plot options are ignored. And if you ask to integrate sin(3.1415926*x) from 0 to 1, then it works again. Is there a work-around?</p>150094Sun, 04 Aug 2013 21:40:03 ZJ RodJ RodCalculus Study guide disappointment
http://www.mapleprimes.com/questions/149405-Calculus-Study-Guide-Disappointment?ref=Feed:MaplePrimes:Tagged With calculus
<p>I got Maple 17 a few weeks ago and it has been helpful in my learning of calculus, but not as much as I had hoped.</p>
<p> </p>
<p>I also bought the Calculus study guide which is a big disappointment. For example, I tried using the integration methods tutor for the integral cos(5x).</p>
<p>The correct answer is 1/5 sin(5x) + C and is found with U-substitution. </p>
<p>With the tutor, I entered cos5x into the function box. cos(5x) does not work....<p>I got Maple 17 a few weeks ago and it has been helpful in my learning of calculus, but not as much as I had hoped.</p>
<p> </p>
<p>I also bought the Calculus study guide which is a big disappointment. For example, I tried using the integration methods tutor for the integral cos(5x).</p>
<p>The correct answer is 1/5 sin(5x) + C and is found with U-substitution. </p>
<p>With the tutor, I entered cos5x into the function box. cos(5x) does not work. The only step that it does allow is the constant rule, and gives the final answer of cos5x x.</p>
<p>Maple itself, gives the correct answer, without the arbitrary constant, which is not a big deal. </p>
<p> </p>
<p>The functions you are allowed to enter in the intergral tutor are very limited, as it is plain text. You are not allowed to use any of the Maple features, unless there is a way to do so that I am unaware of. So anything that is not pretty basic, the tutor is useless.</p>
<p>Is there a way to get Maple to show it's process for getting the answer to an intergral (or anything else really)?</p>
<p> </p>
<p>Thanks!</p>
<p> </p>
<p> </p>149405Fri, 12 Jul 2013 03:51:26 Zbaldysmbaldysmusing integration by parts
http://www.mapleprimes.com/questions/148554-Using-Integration-By-Parts?ref=Feed:MaplePrimes:Tagged With calculus
How to solve with maple using integration by parts the integral?int(sec(x)^(n),x);How to solve with maple using integration by parts the integral?int(sec(x)^(n),x);148554Mon, 17 Jun 2013 17:36:48 ZherclauherclauCalculus. Use Newton's method in Maple to solve
http://www.mapleprimes.com/questions/146628-Calculus-Use-Newtons-Method-In-Maple-To-Solve?ref=Feed:MaplePrimes:Tagged With calculus
<p>Can someone please solve only #19 and #25 using Nwton's method in Maple. I really appreciate it.</p>
<p> </p>
<p>The questions are attached. Thank you</p><p>Can someone please solve only #19 and #25 using Nwton's method in Maple. I really appreciate it.</p>
<p> </p>
<p>The questions are attached. Thank you</p>146628Fri, 03 May 2013 01:58:38 ZfalturaikifalturaikiCalculus Related Rates
http://www.mapleprimes.com/questions/146617-Calculus-Related-Rates?ref=Feed:MaplePrimes:Tagged With calculus
<p>You have been asked to design a one-liter can shaped like a right circular cylinder. What dimensions will use the least material?</p>
<p>-I really need help on how to correctly plug this into my computer. Thank you in advance.</p><p>You have been asked to design a one-liter can shaped like a right circular cylinder. What dimensions will use the least material?</p>
<p>-I really need help on how to correctly plug this into my computer. Thank you in advance.</p>146617Thu, 02 May 2013 19:25:13 ZkarsonhenrykarsonhenryProblem with FunctionChart
http://www.mapleprimes.com/questions/143745-Problem-With-FunctionChart?ref=Feed:MaplePrimes:Tagged With calculus
<p> </p>
<p>The command</p>
<p>f := -.1*(x+3)*(x-1)*(x-3.5):<br>Student[Calculus1][FunctionChart](f,x=-4..4,concavity=[],title="",caption="",gridlines);</p>
<p> </p>
<p>produces different results in Maple 13 and Maple 16.02.</p>
<p>In particular, the concavity=[] option seems to be ignored in 16.</p>
<p>Also, it may be my imagination, but execution seems slower in 16, but I didn't try timing it.</p>
<p>My apologies, if this has already been noted.</p>
<p> <p> </p>
<p>The command</p>
<p>f := -.1*(x+3)*(x-1)*(x-3.5):<br>Student[Calculus1][FunctionChart](f,x=-4..4,concavity=[],title="",caption="",gridlines);</p>
<p> </p>
<p>produces different results in Maple 13 and Maple 16.02.</p>
<p>In particular, the concavity=[] option seems to be ignored in 16.</p>
<p>Also, it may be my imagination, but execution seems slower in 16, but I didn't try timing it.</p>
<p>My apologies, if this has already been noted.</p>
<p> </p>
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<p> </p>143745Fri, 22 Feb 2013 05:26:54 Zbpollinabpollina