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    Finding equation of tangent plane & normal line to a given surface

    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...
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    How to use clairaut's theorem with 3rd order partial derivatives

    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...
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    Position vector perpendicular to tangent vector yields a sphere

    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...
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    Proof for a vector limit?

    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...
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    Magnetic energy density & inductance of a current carrying wire

    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...
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    Need help finding the electric fields in a coaxial cable with charged conductors

    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...