Math Is Fun Forum

Angel Rox

Member

Registered: 2008-11-10

Posts: 15

need help Urgently.. Time till tommorow :(

Q1 - Use chain rule to find df/dx , df/dy

For f(r,s,v) = r^3 + s + v^2  ,  where r = xe^y  , s = ye^x and v = x^2 y

Q2 - Spherical coordinates of a point are (4 , π/6 , π/2)

a - Convert spherical coordinates to rectangular coordinates

b - Convert spherical coordinates to cylinderical coordinates

c - Verify your answer by converting back spherical coordinates from anyone of these, that is , either from rectangular or cylinderical coordinates.

I need detailed answer for Question no. 1 coz i dont know how to start it.. and for Question 2 just hints for that .. Thanks in advance

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: need help Urgently.. Time till tommorow :(

The chain rule lets you differentiation an equation in one variable, with respect to a different one differentiable in that variable. by that i mean for example:

Since you have no equation with y in x, you will end up with equations in dy/dx and dx/dy respectively:

starting off with the sub-functions, and applying product rule:

then to the full function:

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Angel Rox

Member

Registered: 2008-11-10

Posts: 15

Re: need help Urgently.. Time till tommorow :(

Thanx alot dear... It was really helpful... Thanks once again!

Angel Rox

Member

Registered: 2008-11-10

Posts: 15

Re: need help Urgently.. Time till tommorow :(

and yeah in Q2 .. plz correct my answer ..

•    Assuming the spherical coordinates are (r,theta,phi), rectangular coordinates are:
x=r sin(theta)cos(phi)=4 * sin(3.14/2) cos(3.14/6)=3.464
y=r sin(theta)sin(phi)=4 * sin(3.14/2) sin(3.14/6)=2
z=r cos(theta)=4 * cos(3.14/2)=0

Cylindrical coordinates are:
rho = r sin(theta)=4 * sin(3.14/2)=4
phi = phi=3.14/6
z= r cos (theta)=4 * cos(3.14/2)=0

To convert back from cylindrical coordinates
r=sqrt{rho^2+z^2}=rho=4
theta=atan2 {rho,z}=atan2(4,0)=3.14/2
phi=phi=3.14/6

Adnan

Guest

Re: need help Urgently.. Time till tommorow :(

dear please splove it

By considering different path approach, find whether  limt((x,y) -> (0,0)) ((xy3)/x2y4))   exist or not.