Recent content by sibiryk

Yes, my mistake I thought of tangent vector to a surface. Why should I dot f(x,y) if I have f(x,y,z)? Still confused.

I think it's the angle between unit vector and tangent vector to f at Po. If I'm correct, I'm not sure how should I put it on a paper.

The growth is greatest when angle equals zero.

I have f(x,y,z)=(x^2)y-x(e^z) and point Po=(2,-1,pi) I need to find a) gradient at point Po ( done) b) Rate of change of f at point Po in the direction of vector u=i-2j+k (it's also done) c) Unit vector in the direction of fastest growth of f at Po. I can't find formulas for a last on...

It's not a book. I think that professor set this up himself. It looks weird and also confuse me. Makes me think that I was doing some thing wrong. I got zero in both cases.

Evaluate volume integral f=x over sphere interior. Sphere at z>o, center at 0,0,0 and R=2. It looks to me pretty much the same as previous problem. It is only one extra integral from 0 to R= 2 for variable r , and dV instead of dA. Am I correct?

Yes, I set limits as you say.My second problem in homework requires to do the same with volume integral. Same conditions. I also got zero. Would you think it will be the same for survace and for volume integrals?

I'll try that but what about y? Is my f=x parameterization correct?

The integral is too complex if I go with Cartesian coordinates. I parameterized sphere: x=r*cos(phi)*sin(theta); y=r*sin(phi)*sin(theta); y=r*cos(theta) From here I found that dA=(r^2)*sin(theta) Function g(x,y,z)=x I alco put in spherical coordinates as x=r*cos(phi)*sin(theta) (I'm not...

Do you want to say that would be zero?

I started with sphere parametrization: [tex]\P=rcos(\phi)sin(\theta)i+rsin(\phi)sin(\theta)j+rcos(\theta)k[\tex] edit: and I tried latex for a first time and it doesn't work.

Are you talking about special case when surface is flat? If so, I don't think it would work here. Semi sphere is at z>0 with center at (0,0,0) and radius R=2.

I need to evaluate the surface integral of f=x over a semi sphere. I know how to evaluate surface integral of a semi sphere but what are my steps in this case. As I found from books I should double integrate f = x with semi sphere limits. The problem is that I don't know how to start and...

Ok. I integrated equation that give the distance. I got Integral ((cos^2(2t)+6sin^2(2t))^0.5)*dt integral from 0 to pi Did I get it right?

I need to find it using curve integral