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1. Multivariable Functions - stationary points

I have the partial derivatives: fx(x,y)=(2y^2-2xy-x^2+6)/(x^2+2y^2+6)^2 fy(x,y)=(-2y^2-4xy+x^2+6)/(x^2+2y^2+6)^2 Now, for a stationary point, both these equations are equal to zero. I then have to solve these simultaneously to find values for x, which will in turn give me values for...
2. Multivariable Functions - stationary points

Homework Statement For: f(x,y)=(x+y)/(x^2+2y^2+6) Find the stationary points of f Homework Equations The Attempt at a Solution To find a stationary point the first partial derivative must equal zero, correct? I've found the first partial derivatives using the quotient...
3. Multivariable functions - chain rule

My sheet's telling me it should be u=x+y, v=xy, but let's just say it's u=xy and v=x+y for the hell of it. How would you go about solving this problem now?
4. Multivariable functions - chain rule

You're right. It should be u=x+y This still doesn't help me though. I may be wrong, but I've got: dz/dx=dz/du.du/dx+dz/dv.dv/dx dz/dy=dz/du.du/dy+dz/dv.dv/dy as my partial fractions. But how do I get my dz/du and dz/dv when I have z=f(u,v) and not, for example, z=f(u,v)=2u+3v^2 - I'm...
5. Total differential

Homework Statement For: z(x,y)=(x^2)y-3y Find \Deltaz and dz when x=4, y=3, \Deltax=-0.01, \Deltay=0.02 Homework Equations The Attempt at a Solution I got the partial derivatives: df/dx=2xy, and df/dy=x^2-3 and solved dz=0.02 However, I don't know how to find \Deltaz
6. Multivariable functions - chain rule

Homework Statement Since both my questions are on the same topic, i'll throw them both in here 1. Find dz/dt for z=(x^2)(t^2), x^2+3xt+2t^2=1 2. Show that if u=xy, v=xy and z=f(u,v) then: x.dz/dx-y.dz/dy=(x-y)dz/dv Homework Equations The Attempt at a Solution 1. I only...
7. .Determining Convergence/Divergence of 100n/2^n with Ratio Test

Homework Statement Use the ratio test to determine convergence or divergence of 100n/2^n Homework Equations p= lim┬(n→∞)[a_(n+1)/a_n] p<1 ,convergent p>1 ,divergent p=1 ,ratio test fails The Attempt at a Solution I'm not even sure if I'm doing this right, but i get...
8. Integration by Parts

Homework Statement Use integration by parts to find: y=... if dy=arcsinh(x) dx Homework Equations int(v.du)=uv-int(u.dv) The Attempt at a Solution I understand how to perform integration by parts. My problem here is, what are my 'v' and 'du'?
9. Hyperbolic Functions

Homework Statement Given the trigonometric identity cos(x+y)... use Osborn's rule to write down the corresponding identity for cosh(x+y)... Use the definitionis of the hyperbolic functions to prove this identity Homework Equations The Attempt at a Solution I can use Osborns rule...
10. Repeated Eigenvalues

Homework Statement Obtain the eigenvalues and corrosponding eigenvectors for the matrix: [2,2,1;1,3,1;1,2,2] Homework Equations The Attempt at a Solution I can solve for the eigenvalues, 5, 1, and 1 I can solve the eigenvalue 5 for the eigenvector B[1;1;1] Yet somehow, the...
11. Help with Eigenvectors

So, you're telling me that I need to solve y in terms of x from that (very nice) matrix set up, then I can sub in ANY number for x that I want to get my eigenvector and have the right answer? Wouldn't this result in an infinite number of correct eigenvectors? Actually, don't worry about that, I...
12. Help with Eigenvectors

Homework Statement Find the eigenvalues and correspointing eigenvectors of the matrix: [1,1;1,1] Homework Equations The Attempt at a Solution I can solve the determinant to get the eigenvalues: e1=2, e2=0, and from here I am supposed to sub these values back into my matrix...
13. Line Perpendicular to plane

Homework Statement Find the line ... . Show that it is perpendicular to the plane A and find the angle that the line makes with the plane B Homework Equations The Attempt at a Solution I've found the line, but how do I go about showing it's perpendicular and finding the angle?