Review of Basic Maple Commands

PUT SOMETHING TO TEST LINE FEED KEY. Please submit your work as a Maple report. If you have never prepared a Maple report please see the Maple tutorial for instructions.

1. 1. Plot the the following curves - play with the various options to get as good a picture as you can. (i) (Folium of Descartes), (ii) (Astroid), (iii) (Three-leaved rose), (iv) (Parabola).
   2. Display the Folium of Descartes and the Astroid in the same picture coloring them differently. Determine the approximate location of their point of intersection in the second quadrant. Zoom in by changing the view option to determine the point of intersection accurate to two places after the decimal.
   3. Using the fsolve command find the coordinates of this point of intersection numerically. Was your answer in (b) accurate enough? If not then zoom in more in (b).
2. Let . Find the value of A,B,P,Q,R so that
   
   
3. Find all solutions of the system of equations
   
   Then compute the value of at the solution where z is the largest.
4. Consider the expression
   
   Write the above as a polynomial in x and determine the coefficient of . Also, write the above as a multinomial in the variables x and and determine the coefficient of .
5. Find the sum of the first 1000, 2000, 3000 terms of the series
   
   accurate to 8 digits.

 
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