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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?