04/06/13

Compute the linear approximation?
Compute the linear approximation of f(x, y)=sqrt(x^2+y^2) at (3, 0). Answer: L(x, y)=x
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04/04/13

Find equations of the normal line?
Find equations of the normal line to z=sinx cosy at (0, pi, 0). Answer: x=-t, y=pi, z=-t. Fx=cosx cosy Fy=-sinx siny  
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04/03/13

Find all points where f(x, y)=4xy+sin3x^2*y is continuous.
Find all points where f(x, y)=4xy+sin3x^2*y is continuous. The answer is All x, y. But how to get there?
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04/01/13

Find the principal unit normal vector?
Find the principal unit normal vector to the curve defined by r(t)=<t, t^2>. T(t)=1/sqrt(1+4t^2)i+2t/sqrt(1+4t^2)j I need to find T'(t) using quotient rule but don't know how. Show your steps. more
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03/31/13

Find the curvature?
Find the curvature of r(t)=<e^-2t, 2t, 4>. r'(t)=<-2e^-2t, 2, 0> What to do next? Show your steps.
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03/29/13

Use Gauss' Law for Electricity to find the total charge?
Use Gauss' Law for Electricity to find the total charge in the cone y=sqrt(x^2+z^2) for E=<2xy, y^2, 5xy>. (Answer: 0) I've set up the triple integral of 4y dV and the formula for volume of... more
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03/29/13

Use Gauss' Law for Electricity to find the total charge?
Use Gauss' Law for Electricity to find the total charge in the hemisphere z=sqrt(R^2-x^2-y^2) for E=<4x-y, 2y+z, 3xy>. (Answer: 4pi*Eo*R^3) The divergence is 6, I've set up the triple... more
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03/28/13

Use Stokes' Theorem to compute the surface integral?
Use Stokes' Theorem to compute the surface integral where S is the portion of the tetrahedron bounded by x+y+2z=2 and the coordinate planes with z>0, n upward, F=<zy^4-y^2, y-x^3, z^2>.... more
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03/27/13

Find the flux of F over Q where Q is bounded?
Find the flux of F over Q where Q is bounded by 3x+2y+z=6 and the coordinate planes, F=<y^2*x, 4x^2*sin(z), 3>. (Answer: 27/5). The divergence of the vector field is y^2, which is what I've... more
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03/26/13

Find the flux of F over Q where Q is bounded?
Find the flux of F over Q where Q is bounded by z=sqrt(x^2+y^2), x^2+y^2=1 and z=0, F=<y^2, x^2*z, z^2>. (Answer: pi/2) The divergence of the vector field is 2z, which is what I've found.... more
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03/25/13

Find the flux of F over Q where Q is bounded?
Find the flux of F over Q where Q is bounded by z=sqrt(x^2+y^2) and z=sqrt(2-x^2-y^2), F=<x^2, z^2-x, y^3>. (Answer: 0)   I know the integrand is 2x and I need to integrate 2x dV but how do... more
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03/24/13

Use the Divergence Theorem to compute the surface integral?
Use the Divergence Theorem to compute the surface integral where Q is bounded by z=x^2+y^2 and z=4, F=<x^3, y^3-z, xy^2>. (Answer: 32pi) The divergence of the vector field is 3x^2+3y^2,... more
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03/24/13

Use the Divergence Theorem to compute the surface integral?
Use the Divergence Theorem to compute the surface integral where Q is the cube -1<=x<=1, -1<=y<=1, -1<=z<=1, F=<4y^2, 3z-cosx, z^3-x>. (Answer: 8) The divergence of the... more
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03/23/13

Use the Divergence Theorem to compute the surface integral?
Use the Divergence Theorem to compute the surface integral where Q is bounded by x+y+2z=2 (first octant) and the coordi-nate planes, F=<2x-y^2, 4xz-2y, xy^3>. (Answer: 0) The divergence for... more
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03/21/13

Compute the surface area?
Compute the surface area of the portion of the plane 3x+y+2z=6 inside the cylinder x^2+y^2=4. (Answer: 2pi*sqrt(14)) The formula for the surface area of a cylinder is A=2pi*r^2+2pi*r*h But how do I... more
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03/20/13

Compute the surface area?
Compute the surface area of the portion of the cone z=sqrt(x^2+y^2) below the plane z=4. (Answer: 16pi*sqrt(2))
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03/18/13

Compute the work done?
Compute the work done by the force field F(x, y)=<2, x> where C is the portion of y=x^2 from (0, 0) to (1, 1).
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