” MACM 204课程程序 写作、c/c++，Java，Python程序Assignment 1MACM 204Fall 2020The purpose of this assignment is to learn the basics of Maple: how to input formulas, how to graphfunctions, solve equations, calculate derivatives and integrals, and to program some loops.The assignment is due Tuesday September 29th at 11:00am. Do all calculations in Maple in a singleworksheet. Separate clearly your solutions for each question (use text headings Question 1, Question 2,… ). Export the worksheet as PDF and upload a single PDF file to the Crowdmark link that youreceived by e-mail.Write the assignment number, Course number, your name and student number on top of the Mapleworksheet.Question 1Consider the function Construct a plot of [ ] on the samegraph for the domain .Read the help page for ?plot,options. Using the appropriate options, create a legend for theplot, and add a title.Question 2Using the evalf command, calculate the following values to 20 decimal places., =1.648…, 1.912…, … and …Question 3Consider the polynomials and andGraph each separately on a suitable domain for so that we can see all real roots.Now factor the polynomials using the factor command.Why does the factor command not factor them into linear factors?Now, using solve, solve for the roots. Using Maple, verify that the 4 roots of the polynomial g arecorrect.MACM 204课程作业 写作、c/c++，Java，PythonNow, using fsolve, solve for numerical approximations of the roots, including the complex roots.Read the help page for ?fsolve to find out how to get the complex roots.Question 4Shown in the plot below is a plot of on the domain -2.5 2. Shown alsois the line tangent to at .Use Maple to reproduce the plot. Do this by using the diff and eval commands to compute the slopeof at so you can determine the equation for the tangent line.Now express the area enclosed by the tangent line and as a definite integral.Evaluate the definite integral using Maple.Question 5Consider the two equations and which are the equations of an elliptic curveand a circle. Graph the Two curves together using the implicitplot command in the plots package.Improve the smoothness of the plot using the grid option. The circle will appear distorted. Find outfrom ?plot,options how to scale the axes so that the circle looks like a circle (so that the plot lookslike the figure below).You can read off from the plot roughly where the curves intersect.Use Maple to calculate the intersection points accurately.Do this by solving two equations simultaneously.Question 6Calculate the following antiderivatives in Maple.(i) (ii) (iii) .To check that the results are correct, use Maple to differentiate each antiderivative.Question 7Suppose you are given a Maple list L of numbers which are the roots of a polynomial . Write aMaple for loop that constructs the polynomial. For example, if L = then the value ofshould be the polynomial .Question 8Using a Maple loop, and the isprime command, find the first prime .Question 9Consider the odd primes 3, 5, 7, 11, 13, 17, 19, etc.Let S be the odd primes congruent to 1 mod 4 and T be the odd primes congruent to 3 mod 4.So S = 5, 13, 17, 29, etc. and T = 3, 7, 11, 19, 23, etc.Suppose we go through the Odd primes in order counting the number of primes in S and T.So at the first step S = { } and T = {3} so T has more primes than S.At the second step S = {5} and T = {3} so S and T have the same number of primes.At the third step S = {5} and T = {3,7} so T has more primes than S again.Here is a little table counting the size of S and T for the first 10 primesPrime 3 5 7 11 13 17 19 23 29 31|S| 0 1 1 1 2 3 3 3 4 4|T| 1 1 2 3 3 3 4 5 5 6Notice that for the first 10 primes. Does it ever happen that ? Yes, it does.When? How often?Using the builtin nextprime Command write a loop that counts and for primes up to 10^6and prints out the the first Time and, at the end, how oftenQuestion 10Let . Recall that the value of A may be approximated by the Trapezoidal rule on nintervals of width using the formula.For and , calculate using Maple to 10 decimal places by usingMaples integration Command. Now using a Maple loop, calculate and using 10 digitarithmetic (the default) .如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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