Homework Statement
Find equations of the tangent plant and the normal line to x-z=4arctan(yz) at (1+∏, 1, 1)
Homework Equations
The Attempt at a Solution
I took the partials and got fx=0 fy=0 fz=(-4y)/((yz)2+1) so for the plane i got -2z-2=0 and for the normal line I got .5z-2=0...
Homework Statement
Use Clairaut's Theorem to show that is the third order partial derivatives are continuous, then fxxy=fyxy=fyyz
Clairaut's Theorem being: fxy(a,b)=fyx(a.b)
Homework Equations
fxyy=d/dy(d2f/dydx)=d^3f/dy^2dx
The Attempt at a Solution
Tried to differentiate...
Homework Statement
If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with center the origin.
Homework Equations
-1/r'(t)= slope of position vector
x^{2}+y^{2}=1
The Attempt at a...
proof for a vector limit??
Homework Statement
Show that the lim(t-->a)r(t)=b. if and only if for every \epsilon>0 there is a number \delta>0 such that if 0<|t-a|<\delta then |r(t)-b|<\epsilon
This is asking to prove the limit of a vector function.
It seems to me that within the question...
Homework Statement
A long straight wire of radius r=a carries a current I uniformly distributed over its cross section. Show that the magnetic energy per unit length (energy density u=B^2/2mu) is given by \mi_{o}\ =\ 4\pi\ \timesI^2\ 10^{-7}/16pi. What is the contribution that a single long...
Homework Statement
A coaxial cable consists of a long solid inner cylindrical conductor, radius a, and a thin outer cylindrical conductor of average radius b>a. Suppose the inner conductor has a line charge density of +lambda while the outer conductor has a uniformly distributed charge of...