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I've got a set

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)

and consequently obtained the equations:

x/sqrt(x^2+y^2+z^2) + 2*x*L1+L1=0

y/sqrt(x^2+y^2+z^2) + 2*y*L1+2*y*L2=0

z/sqrt(x^2+y^2+z^2)+2*L1+2*L2*z=0

for which I've set up
eqn1,eqn2,eqn3 as the three equations and vars:=x,y,z

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.)

How should I implement that?

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 
for
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.

2.

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

 

 

 

 

Hello,

 

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 

Hello,

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
Set
"mylist = []."

Start at
x = 0
and
y = 0.

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

Phase B
Repeat the following until
x^2>n

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:

x'(t)=2x(t)+3y(t)

y(t)=-3x(t)-2y(t)

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
f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz
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?

 

2.

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 :

limit((1+y)^(x-1)/(1-cos((x-1)^2+y^2)^(1/4)),{x=1,y=0});

 

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?

(http://imgur.com/SDBP0sw)


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))

Digits:=15;

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! :)

Hello,

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

 

thank you very much.

 

 

hello, 

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

R:=rand(1..50)

seq(R(1..50),i=1..20)

L:=[%]

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

locali;

maxv:=L[i];

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.

Thanks

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

 

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