MaplePrimes - Questions and Posts tagged with homework
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en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 04 Mar 2015 12:47:23 GMTWed, 04 Mar 2015 12:47:23 GMTThe most recent questions and posts on MaplePrimes tagged with homeworkhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with homework
http://www.mapleprimes.com/tags/homework
Multidimensional Limit evaluation
http://www.mapleprimes.com/questions/203621-Multidimensional-Limit-Evaluation?ref=Feed:MaplePrimes:Tagged With homework
<p><strong>f:=sin((x-1)*(y+3))/(exp((x-1)^2+(y+3)^2)-1);</strong><br><strong>limit(f,{x=1,y=-3});<br><br></strong></p>
<p><strong><br></strong>On running the above code, I don't get a result. I don't understand why, and what are some of the underlying math principles that I would have to use to evaluate the limit of f at (1,-3) if I were to solve this question on paper?</p><p><strong>f:=sin((x-1)*(y+3))/(exp((x-1)^2+(y+3)^2)-1);</strong><br><strong>limit(f,{x=1,y=-3});<br><br></strong></p>
<p><strong><br></strong>On running the above code, I don't get a result. I don't understand why, and what are some of the underlying math principles that I would have to use to evaluate the limit of f at (1,-3) if I were to solve this question on paper?</p>203621Wed, 04 Mar 2015 06:29:56 ZGPYGPYfinding values at which a limit exists/does not exist
http://www.mapleprimes.com/questions/203620-Finding-Values-At-Which-A-Limit-Existsdoes?ref=Feed:MaplePrimes:Tagged With homework
<p>I need to find where the limit of the function:</p>
<p>{1-cos(x*y^3)}/(x^2+y^6)^(1+a) exists/does not exists for different values of a, given 0<=a<=1 and as (x,y)->(0,0).</p>
<p>I've tried writing a procedure that changes a in particular increments but that is clearly not the most efficient way. Are there any rules of limits that I should be using?</p>
<p> </p><p>I need to find where the limit of the function:</p>
<p>{1-cos(x*y^3)}/(x^2+y^6)^(1+a) exists/does not exists for different values of a, given 0<=a<=1 and as (x,y)->(0,0).</p>
<p>I've tried writing a procedure that changes a in particular increments but that is clearly not the most efficient way. Are there any rules of limits that I should be using?</p>
<p> </p>203620Wed, 04 Mar 2015 06:14:54 ZGPYGPYsolving a system of equations involving lagrange multipliers
http://www.mapleprimes.com/questions/203619-Solving-A-System-Of-Equations-Involving?ref=Feed:MaplePrimes:Tagged With homework
<p>I've got a set</p>
<p>E:={(x,y,z): x^2+y^2=-2*z-x, z^2+y^2=1} and need to find points of E which have minimal or maximal distance from (0,0,0). I've set up the Lagrangian as F:=sqrt(x^2+y^2+z^2) + L1(x^2+y^2+2z+x)+L2(z^2+y^2-1)</p>
<p>and consequently obtained the equations:</p>
<p>x/sqrt(x^2+y^2+z^2) + 2*x*L1+L1=0</p>
<p>y/sqrt(x^2+y^2+z^2) + 2*y*L1+2*y*L2=0</p>
<p>z/sqrt(x^2+y^2+z^2)+2*L1+2*L2*z=0</p>
<p>for which I've set up <br>eqn1,eqn2,eqn3 as the three equations and vars:=x,y,z</p>
<p>and used solve() but I'm not getting the right answer( I need to first express x,y,z in terms of L1, L2 and then get values for L1 and L2 by substituting in the constraints and eventually get values of x,y,z.)</p>
<p>How should I implement that?</p><p>I've got a set</p>
<p>E:={(x,y,z): x^2+y^2=-2*z-x, z^2+y^2=1} and need to find points of E which have minimal or maximal distance from (0,0,0). I've set up the Lagrangian as F:=sqrt(x^2+y^2+z^2) + L1(x^2+y^2+2z+x)+L2(z^2+y^2-1)</p>
<p>and consequently obtained the equations:</p>
<p>x/sqrt(x^2+y^2+z^2) + 2*x*L1+L1=0</p>
<p>y/sqrt(x^2+y^2+z^2) + 2*y*L1+2*y*L2=0</p>
<p>z/sqrt(x^2+y^2+z^2)+2*L1+2*L2*z=0</p>
<p>for which I've set up <br>eqn1,eqn2,eqn3 as the three equations and vars:=x,y,z</p>
<p>and used solve() but I'm not getting the right answer( I need to first express x,y,z in terms of L1, L2 and then get values for L1 and L2 by substituting in the constraints and eventually get values of x,y,z.)</p>
<p>How should I implement that?</p>203619Wed, 04 Mar 2015 05:06:17 ZGPYGPYwriting procedures
http://www.mapleprimes.com/questions/203585-Writing-Procedures-?ref=Feed:MaplePrimes:Tagged With homework
<p>1. a procedure quadsumstats whose input is an integer n. This procedure should return a list of length </p>
<p>n whose kth entry is the number of solutions to <br>x^2 + y^2 = k <br> for <br> 1 <= k and k <= n</p>
<p>I am sort of confused as to how to construct that list of length n and how to obtain integer solutions to the equation in maple.</p>
<p>2.</p>
<p>a procedure firstCount(k) that finds the first integer <br> n<br> with <br> k<br> representations as <br> "x^2+y^2= n." What does it mean for an integer to have k representations?</p>
<p> </p>
<p> </p>
<p> </p>
<p> </p><p>1. a procedure quadsumstats whose input is an integer n. This procedure should return a list of length </p>
<p>n whose kth entry is the number of solutions to <br>x^2 + y^2 = k <br> for <br> 1 <= k and k <= n</p>
<p>I am sort of confused as to how to construct that list of length n and how to obtain integer solutions to the equation in maple.</p>
<p>2.</p>
<p>a procedure firstCount(k) that finds the first integer <br> n<br> with <br> k<br> representations as <br> "x^2+y^2= n." What does it mean for an integer to have k representations?</p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>203585Fri, 27 Feb 2015 00:25:06 ZGPYGPYHow to write a simple code
http://www.mapleprimes.com/questions/203580-How-To-Write-A-Simple-Code?ref=Feed:MaplePrimes:Tagged With homework
<p>Hello,</p>
<p><span> </span></p>
<p><span>How can I write a code to calculate the Rieman Sum for y=x^1/2 [0..4] using </span></p>
<p><span>left hand rule and 100 subdivision.</span></p>
<p><span>Thank you </span></p><p>Hello,</p>
<p><span> </span></p>
<p><span>How can I write a code to calculate the Rieman Sum for y=x^1/2 [0..4] using </span></p>
<p><span>left hand rule and 100 subdivision.</span></p>
<p><span>Thank you </span></p>203580Thu, 26 Feb 2015 06:34:16 ZJahani_21Jahani_21How do i write a code for a procedure
http://www.mapleprimes.com/questions/203577-How-Do-I-Write-A-Code-For-A-Procedure?ref=Feed:MaplePrimes:Tagged With homework
<p>Hello,</p>
<p>i need help!!</p>
<p>write a procedure for the taylor series sin (x) and plot it in the range (-2pi to 2 pi)</p>
<p>use 20 term iterations in the taylor series approximation.</p>
<p>Thank you very much for your help.... </p><p>Hello,</p>
<p>i need help!!</p>
<p>write a procedure for the taylor series sin (x) and plot it in the range (-2pi to 2 pi)</p>
<p>use 20 term iterations in the taylor series approximation.</p>
<p>Thank you very much for your help.... </p>203577Wed, 25 Feb 2015 23:02:28 ZJahani_21Jahani_21procedure that takes integer n and returns an ordered pair (x,y) of solutions
http://www.mapleprimes.com/questions/203572-Procedure-That-Takes-Integer-N-And-Returns-An-Ordered-Pair-xy?ref=Feed:MaplePrimes:Tagged With homework
<p>I need to write a procedure that does the following :</p>
<p>Write a procedure quadsum whose input is an integer n and whose output is a list of pairs of solutions [x,y] to the above formula.</p>
<p>Your procedure should implement the following algorithm.</p>
<p>1 Initialization<br>Set <br> "mylist = []."</p>
<p>Start at <br> x = 0<br> and <br> y = 0.</p>
<p>2 Phase A<br>Increment both <br> x<br> and <br> y<br> until <br> "x^2+y^2 >=n."</p>
<p>Phase B<br>Repeat the following until <br>x^2>n</p>
<p>If you are above the circle <br> x^2 + y^2 = n<br> then go down in unit steps until you are on or below the circle.</p>
<p>If you are on the circle, add the point to the list <br> "mylist. "<br> <br> If you are on or below the circle <br> x^2 + y^2 = n<br> then go one step to the right. My procedure is as follows: but it runs into an infinite loop(most probably because of the while loop defined inside the while loop). What am I doing incorrectly?</p>
<p>I have atta<img src="/view.aspx?sf=203572_question/numtheoryproc.PNG" alt=""></p>
<p> </p><p>I need to write a procedure that does the following :</p>
<p>Write a procedure quadsum whose input is an integer n and whose output is a list of pairs of solutions [x,y] to the above formula.</p>
<p>Your procedure should implement the following algorithm.</p>
<p>1 Initialization<br>Set <br> "mylist = []."</p>
<p>Start at <br> x = 0<br> and <br> y = 0.</p>
<p>2 Phase A<br>Increment both <br> x<br> and <br> y<br> until <br> "x^2+y^2 >=n."</p>
<p>Phase B<br>Repeat the following until <br>x^2>n</p>
<p>If you are above the circle <br> x^2 + y^2 = n<br> then go down in unit steps until you are on or below the circle.</p>
<p>If you are on the circle, add the point to the list <br> "mylist. "<br> <br> If you are on or below the circle <br> x^2 + y^2 = n<br> then go one step to the right. My procedure is as follows: but it runs into an infinite loop(most probably because of the while loop defined inside the while loop). What am I doing incorrectly?</p>
<p>I have atta<img src="/view.aspx?sf=203572_question/numtheoryproc.PNG" alt=""></p>
<p> </p>203572Wed, 25 Feb 2015 15:43:45 ZGPYGPYhow to determine the nature of an equilibrium point using eigen values
http://www.mapleprimes.com/questions/203568-How-To-Determine-The-Nature-Of-An-Equilibrium?ref=Feed:MaplePrimes:Tagged With homework
<p>If I have the following system of first order diff eq's:</p>
<p>x'(t)=2x(t)+3y(t)</p>
<p>y(t)=-3x(t)-2y(t)</p>
<p>then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:</p>
<p>if the eigenvalues are of the same sign- eq point is a node</p>
<p>if they are of opposite signs- eq point is a saddle</p>
<p>if they are pure imaginary- eq point is a center</p>
<p>if they are complex conjugates- eq. point is a spiral</p>
<p>I've been given these conditions but my text says for a linear system of the form x'=Ax, the eigenvalues of A can be used to identify the nature of the eq. point. I am confused as to whether this applies to the given system as well; I have obtained 5 different trajectories and drawn the phase diagram for the system<img src="/view.aspx?sf=203568_question/phaseDiagram.PNG" alt=""></p><p>If I have the following system of first order diff eq's:</p>
<p>x'(t)=2x(t)+3y(t)</p>
<p>y(t)=-3x(t)-2y(t)</p>
<p>then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:</p>
<p>if the eigenvalues are of the same sign- eq point is a node</p>
<p>if they are of opposite signs- eq point is a saddle</p>
<p>if they are pure imaginary- eq point is a center</p>
<p>if they are complex conjugates- eq. point is a spiral</p>
<p>I've been given these conditions but my text says for a linear system of the form x'=Ax, the eigenvalues of A can be used to identify the nature of the eq. point. I am confused as to whether this applies to the given system as well; I have obtained 5 different trajectories and drawn the phase diagram for the system<img src="/view.aspx?sf=203568_question/phaseDiagram.PNG" alt=""></p>203568Wed, 25 Feb 2015 03:09:17 ZGPYGPYto show left null space and column space are orthogonal
http://www.mapleprimes.com/questions/203556-To-Show-Left-Null-Space-And-Column-Space?ref=Feed:MaplePrimes:Tagged With homework
<p>I have a matrix A for which the basis of the left null space using NullSpace() is the empty set {} while the column space is {e1,e2,e3}. By definition, we need every vector in col space . every vector in basis of left null space =0 but how would I show that in this case? Can I determine another basis for the left null space?</p><p>I have a matrix A for which the basis of the left null space using NullSpace() is the empty set {} while the column space is {e1,e2,e3}. By definition, we need every vector in col space . every vector in basis of left null space =0 but how would I show that in this case? Can I determine another basis for the left null space?</p>203556Mon, 23 Feb 2015 11:14:09 ZGPYGPYminimum of a function using determinants
http://www.mapleprimes.com/questions/203551-Minimum-Of-A-Function-Using-Determinants?ref=Feed:MaplePrimes:Tagged With homework
<p>Determine using determinants the range of values of a (if any) such that<br> f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz<br> has a minimum at (0,0,0).</p>
<p>From the theory, I understand that if the matrix corresponding to the coefficients of the function is positive definite, the function has a local min at the point. But, how do I get the range of values of a such that f is a min? Is this equivalent to finding a such that det(A) > 0?</p>
<p> </p>
<p>2.</p>
<p>Now modify the function to also involve a parameter b: g(x,y,z)=bx^2+2axy+by^2+4xz-2a^2yz+2bz^2. We determine conditions on a and b such that g has a minimum at (0,0,0). <br>By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.</p>
<p>Which region corresponds to a local minimum?</p>
<p>Now determine region(s) in the (a,b) plane where g has a local maximum.</p>
<p>I don't understand this part at all..</p><p>Determine using determinants the range of values of a (if any) such that<br> f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz<br> has a minimum at (0,0,0).</p>
<p>From the theory, I understand that if the matrix corresponding to the coefficients of the function is positive definite, the function has a local min at the point. But, how do I get the range of values of a such that f is a min? Is this equivalent to finding a such that det(A) > 0?</p>
<p> </p>
<p>2.</p>
<p>Now modify the function to also involve a parameter b: g(x,y,z)=bx^2+2axy+by^2+4xz-2a^2yz+2bz^2. We determine conditions on a and b such that g has a minimum at (0,0,0). <br>By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.</p>
<p>Which region corresponds to a local minimum?</p>
<p>Now determine region(s) in the (a,b) plane where g has a local maximum.</p>
<p>I don't understand this part at all..</p>203551Mon, 23 Feb 2015 00:41:38 ZGPYGPYFinding local minima and maxima of a function of two variables
http://www.mapleprimes.com/questions/203496-Finding-Local-Minima-And-Maxima-Of-A?ref=Feed:MaplePrimes:Tagged With homework
<p>I need to find the local maxima and minima of f(x,y)=x(x+y)*e^(y-x). I have tried to look for an appropriate method that I could use to achieve this, but got stuck. I also don't quite understand the math behind tying to obtain the local maxima and minima for a function of this type.</p><p>I need to find the local maxima and minima of f(x,y)=x(x+y)*e^(y-x). I have tried to look for an appropriate method that I could use to achieve this, but got stuck. I also don't quite understand the math behind tying to obtain the local maxima and minima for a function of this type.</p>203496Mon, 16 Feb 2015 09:12:45 ZGPYGPYmultidimensional limits
http://www.mapleprimes.com/questions/203495-Multidimensional-Limits?ref=Feed:MaplePrimes:Tagged With homework
<p>I'm trying to evaluate the multidimensional limit: </p>
<p>(1+y)^(x-1)-1/(1-cos((x-1)^2+y^2)^(1/4)) as (x,y)->(1,0) using the limit command :</p>
<p>limit((1+y)^(x-1)/(1-cos((x-1)^2+y^2)^(1/4)),{x=1,y=0});</p>
<p> </p>
<p>but don't seem to get any output. Also, I think the limit for this function doesn't exist or is indeterminate on R2. Where am I wrong?</p><p>I'm trying to evaluate the multidimensional limit: </p>
<p>(1+y)^(x-1)-1/(1-cos((x-1)^2+y^2)^(1/4)) as (x,y)->(1,0) using the limit command :</p>
<p>limit((1+y)^(x-1)/(1-cos((x-1)^2+y^2)^(1/4)),{x=1,y=0});</p>
<p> </p>
<p>but don't seem to get any output. Also, I think the limit for this function doesn't exist or is indeterminate on R2. Where am I wrong?</p>203495Mon, 16 Feb 2015 08:38:37 ZGPYGPYHelp with Taylor Expansions and Polynomials
http://www.mapleprimes.com/questions/203492-Help-With-Taylor-Expansions-And-Polynomials?ref=Feed:MaplePrimes:Tagged With homework
<p>(http://imgur.com/SDBP0sw)</p>
<p><strong><br>Hello, everyone!</strong></p>
<p><strong><br>I was given this week's Maple assignment in my class and I've come across a problem. I'll say this now so I don't get sent away, I am NOT asking for the answer. For this question there is a part A and part B, but also a preliminary check to make sure our code is wokring (as seen in the picture link). The issue I'm here for is that I can't figure out the code for the preliminary check... I've been here for hours and I'm stumped.</strong></p>
<p> </p>
<p><strong>This is my attemp so far; </strong></p>
<p> </p>
<p><strong>f := x^(6*ln(x))</strong></p>
<p><strong>Digits:=15;</strong></p>
<p><strong>T2 := convert(%, polynom)</strong></p>
<p><strong>f_value := evalf(subs(x = 5, T2))</strong></p>
<p> </p>
<p><strong>I'm very confused what to do next in order to get that preliminary test amount of 5121425.461.</strong></p>
<p><strong>Thanks in advance! :)</strong></p><p>(http://imgur.com/SDBP0sw)</p>
<p><strong><br />Hello, everyone!</strong></p>
<p><strong><br />I was given this week's Maple assignment in my class and I've come across a problem. I'll say this now so I don't get sent away, I am NOT asking for the answer. For this question there is a part A and part B, but also a preliminary check to make sure our code is wokring (as seen in the picture link). The issue I'm here for is that I can't figure out the code for the preliminary check... I've been here for hours and I'm stumped.</strong></p>
<p> </p>
<p><strong>This is my attemp so far; </strong></p>
<p> </p>
<p><strong>f := x^(6*ln(x))</strong></p>
<p><strong>Digits:=15;</strong></p>
<p><strong>T2 := convert(%, polynom)</strong></p>
<p><strong>f_value := evalf(subs(x = 5, T2))</strong></p>
<p> </p>
<p><strong>I'm very confused what to do next in order to get that preliminary test amount of 5121425.461.</strong></p>
<p><strong>Thanks in advance! :)</strong></p>203492Sun, 15 Feb 2015 03:59:40 ZVoltageistVoltageisthow to randomly generate 100 numbers and output the number of unique elements
http://www.mapleprimes.com/questions/203475-How-To-Randomly-Generate-100-Numbers?ref=Feed:MaplePrimes:Tagged With homework
<p>Hello,</p>
<p>How can i from a randomly generated 100 numbers, output the number of unique elements...</p>
<p> </p>
<p>thank you very much.</p><p>Hello,</p>
<p>How can i from a randomly generated 100 numbers, output the number of unique elements...</p>
<p> </p>
<p>thank you very much.</p>203475Thu, 12 Feb 2015 14:33:51 ZkevinmaplekevinmapleHow to use a loop to determine the largest integer in the list of 20 random integers
http://www.mapleprimes.com/questions/203474-How-To-Use-A-Loop-To-Determine-The-Largest?ref=Feed:MaplePrimes:Tagged With homework
<p> </p>
<p> </p>
<p>hello, </p>
<p>i need to use only looping to determine the larget integer in my random list...</p>
<p>here is how i put it together, but my result is incorrrect... Please help.</p>
<p>thank you</p>
<p>R:=rand(1..50)</p>
<p>seq(R(1..50),i=1..20)</p>
<p>L:=[%]<br><br></p>
<p>max:=proc(L,maxv : : evaln)</p>
<p>locali;</p>
<p>maxv:=L[i];</p>
<p>for i from 1 to nops(L) do</p>
<p>if eval(maxv)<L[i] then maxv:=L[i]end if;<br>end do;</p>
<p>end proc;</p>
<p> </p><p> </p>
<p> </p>
<p>hello, </p>
<p>i need to use only looping to determine the larget integer in my random list...</p>
<p>here is how i put it together, but my result is incorrrect... Please help.</p>
<p>thank you</p>
<p>R:=rand(1..50)</p>
<p>seq(R(1..50),i=1..20)</p>
<p>L:=[%]<br /><br /></p>
<p>max:=proc(L,maxv : : evaln)</p>
<p>locali;</p>
<p>maxv:=L[i];</p>
<p>for i from 1 to nops(L) do</p>
<p>if eval(maxv)<L[i] then maxv:=L[i]end if;<br />end do;</p>
<p>end proc;</p>
<p> </p>203474Thu, 12 Feb 2015 14:07:57 Zkevinmaplekevinmaple