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1.  a procedure quadsumstats whose input is an integer n. This procedure should return a list of length 

n whose kth  entry is the number of solutions to
x^2 + y^2 = k 
1 <= k and k <= n

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.


a procedure firstCount(k) that finds the first integer
representations as
"x^2+y^2= n." What does it mean for an integer to have k representations?







How can I write a code to calculate the Rieman Sum for  y=x^1/2 [0..4] using 

left hand rule and 100 subdivision.

Thank you 


i need help!!

write a procedure for the taylor series sin (x) and plot it in the range (-2pi to 2 pi)

use 20 term iterations in the taylor series approximation.

Thank you very much for your help.... 

I need to write a procedure that does the following :

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.

Your procedure should implement the following algorithm.

1 Initialization
"mylist = []."

Start at
x = 0
y = 0.

2 Phase A
Increment both
"x^2+y^2 >=n."

Phase B
Repeat the following until

If you are above the circle
x^2 + y^2 = n
then go down in unit steps until you are on or below the circle.

If you are on the circle, add the point to the list
"mylist. "

If you are on or below the circle
x^2 + y^2 = n
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?

I have atta


If I have the following system of first order diff eq's:



then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:

if the eigenvalues are of the same sign- eq point is a node

if they are of opposite signs- eq point is a saddle

if they are pure imaginary- eq point is a center

if they are complex conjugates- eq. point is a spiral

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

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?

Determine using determinants the range of values of a (if any) such that
has a minimum at (0,0,0).

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?



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).
By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.

Which region corresponds to a local minimum?

Now determine region(s) in the (a,b) plane where g has a local maximum.

I don't understand this part at all..

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.

I'm trying to evaluate the multidimensional limit: 

(1+y)^(x-1)-1/(1-cos((x-1)^2+y^2)^(1/4)) as (x,y)->(1,0) using the limit command :



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?


Hello, everyone!

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.


This is my attemp so far; 


f := x^(6*ln(x))


T2 := convert(%, polynom)

f_value := evalf(subs(x = 5, T2))


I'm very confused what to do next in order to get that preliminary test amount of 5121425.461.

Thanks in advance! :)


How can i from a randomly generated 100 numbers, output the number of unique elements...


thank you very much.




i need to use only looping to determine the larget integer in my random list...

here is how i put it together, but my result is incorrrect... Please help.

thank you




max:=proc(L,maxv : : evaln)



for i from 1 to nops(L) do

if eval(maxv)<L[i] then maxv:=L[i]end if;
end do;

end proc;


Not sure exactly how i could achieve this but:

how do i determine the value of k for which the graphs p(x) = x^2+2x+3 and q(x) = k+5x-7x^2 enclose an area of exactly 36?

I have to do it in maple and using i guess area under the curve.


I need to show that the least square solution x that I obtained as x=pseudoinverse(A).b is the solution of Transpose(A).A.x=Transpose(A).b with the smallest norm. I've obtained the norm for the RHS of this expression as well as the norm of x but I'm unsure of how to conclude that this is the lowest possible norm using these values


Hi, Very new to Maple. This is a math assignment, and well I am not exactly sure what is happening. I have had a buddy to help me, but things are not necessarily working. Using Maple17.
This is what I have so far.

de := sin(x)*(diff(y(x), x))+cos(x)*y(x) = Q;
/ d \
sin(x) |--- y(x)| + cos(x) y(x) = Q
\ dx /
Q x + _C1
y(x) = ---------
ab := 75; Q := 2-0.1e-1*ab; M := 4+0.1e-1*ab;
PS := simplify(dsolve({de, y((1/2)*Pi) = M}, y(x)));
-10 x - 38 + 5 Pi
y(x) = - -----------------
8 sin(x)
z := rhs(PS);
-10 x - 38 + 5 Pi
- -----------------
8 sin(x)
N := evalf(subs(x = .4, z));
a := z, x = 0 .. Pi, y = 0 .. 10; b := plots[pointplot]([(1/2)*Pi, M]); c := plots[pointplot]([.4, N]); d := plots[pointplot]([x0, y0]); plots[display]({a, b, c, d});
z, x = 0 .. Pi, y = 0 .. 10
Error, (in plots:-pointplot) points cannot be converted to floating-point values
Error, (in plots:-pointplot) points cannot be converted to floating-point values
Error, (in plots:-pointplot) points cannot be converted to floating-point values
Error, (in plots:-display) expecting plot structures but received: {c, d, z, plots:-pointplot, x = 0 .. Pi, y = 0 .. 10}

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