06/06/13

Compute the curl?
Let F(x, y) be the vector field ((x-y)/(x^2+y^2), (x+y)/(x^2+y^2)). Compute curl(F).
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06/06/13

Help me with this integral?
Use an appropriate change of variables to evaluate the triple integral of (cos(x^2/4+y^2/9+z^2/25)/(sqrt(x^2/4+y^2/9+z^2/25))) dV where R is the region defined by the inequalities... more
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06/06/13

Determine whether the line integral F*ds is path-independent?
Let R be the unit cube defined by 0<=x<=1, 0<=y<=1, 0<=z<=1, and let F(x, y, z)=(x+yz, y+xz, z+xy). Determine whether the line integral F*ds is path-independent.
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06/05/13

Determine all the local minima, local maxima, and saddles of the function?
Determine all the local minima, local maxima, and saddles of the function f(x, y)=x^4-x^2-2xy+y^2. The gradient for f=(4x^3-2x-2y, -2x+2y)=(0, 0) x=y 4x^3-4x=0 x=0, -1, 1 Critical points: (0, 0)... more
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06/03/13

Set up a triple integral?
Set up a triple integral that equals the volume of the intersection of the interior of two cylinders of radius a>0 whose axes intersect at a right angle. HINT: Take one of the cylinders to be:... more
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06/03/13

Find the centroid of the plane?
Find the centroid of the plane region above the curve y=x^4, below the straight line y=x and in the first quadrant.
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06/03/13

Find the average temperature of the body?
A body occupies the region in space inside the cylinder x^2+y^2=4, above the xy plane, and below the surface z=2+x. The temperature at the point (x, y, z) in the body is given by T(x, y, z)=2x.... more
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06/03/13

Find the tangent plane to the ellipsoid?
Find the tangent plane to the ellipsoid x^2+4y^2=169-9z^2 at the point P=(3, 2, 4).
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06/02/13

Find the rate of change?
Find the rate of change of f, df/dt, along the parametric curve x(t)=2t-1, y(t)=3-2t^2 at t=1. The answer is -8 and I need to find df/dt(1).
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06/02/13

What is the gradient?
Consider the function S(H, T, V)=(V+10)e^(-1/H)+(T-80)^2+V^3. What is the gradient of the function S(H, T, V) at the point (1, 81, 3)?
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05/29/13

Please estimate R(3.1, -3.1)?
Let R(x, y) be a function of two variables such that R(3, -3)=4 and the gradient R(3, -3)=<-1, 2>. b) Use the linear approximation or differentials to estimate R(3.1, -3.1).
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05/29/13

Please find fxy?
Find fxy if f(x, y)=xye^(x^2*y).
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05/29/13

Find the maximum and minimum values?
Find the maximum and minimum values of the function f(x, y)=xy^2 subject to the constraint x^2+y^2=4. gradient of f=<y^2, 2xy> gradient of g=<2x, 2y> I'm stucked.
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05/29/13

Find the local maxima, local minima and saddle points?
Find the local maxima, local minima and saddle points of the function f(x, y)=y^3-6xy+8x^2. fx=-6y+16x fy=3y^2-6x -6y+16x=0 3y^2-6x=0 y=8x/3 3(8x/3)^2-6x=0 I'm stucked.
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05/28/13

Find the directional derivative?
Find the directional derivative of f(x, y)=xye^(-xy^2) at the point (1, 1) in the direction <2/sqrt(5), 1/sqrt(5)>. f=<ye^(-y^2), xe^(-2xy)> f(1, 1)=<e, e^-2> u=<2/sqrt(5),... more
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05/26/13

Use Lagrange multipliers to find the shortest distance?
Use Lagrange multipliers to find the shortest distance from the point (2, 0, -3) to the plane x+y+z=1. (x-2)^2+y^2+(z+3)^2 g=x+y+z=1 <2(x-2), 2y, 2(z+3)>=λ<1, 1,... more
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05/26/13

Find y"(0) and y'''(0)?
Let y(t) be a function which satisfies the differential equation y"(t)+(1+t)y'(t)+(1+t+t^2)y(t)=0, y(0)=1, y'(0)=0. Find y"(0) and y'''(0).
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05/25/13

Use Lagrange multipliers to find the points?
Use Lagrange multipliers to find the points on the ellipsoid x^2+y^2-3y+yz-6z+z^2=-5 that are closest and farthest from the xy-plane.
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05/24/13

Write an equation for the tangent plane?
If f(0, -2)=4 and gradient f(0, -2)=<4/5, 12/25>, write an equation for the tangent plane to the surface z=f(x, y) at this point.
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05/24/13

Please evaluate this hard derivative?
Evaluate (d^100/(dx^95 dy^2 dx^3))((y)(e^x)(x)+cos(x)). The answer is 0 but I just seem to get super confused with this problem. Please show the work step by step so I won't get lost. I've work on... more
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05/24/13

Consider the function f(x, y)=y^2-x^2-yx^3.
b) Find the equation of the tangent plane to the graph of z=f(x, y) at the point (1, -1, 1). c) Compute the directional derivative of f at the point (1, -1) in the direction of <3, 1>.
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05/22/13

Please compute this?
Consider the function f(x, y)=y^2-x^2-yx^3. Compute f(1, -1). There's a triangle in front of f(1, -1), an opposite triangle.
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05/22/13

Free Astronomy ebooks?
Can someone please provide me a link for free astronomy textbooks online for high school students that has lots of practice problems? Unfortunately my school doesn't have them.
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05/22/13

Find the equation of the plane?
If the vector function r(t)=<t+2, 2t^2-t+1, 3+t-t^3> is at the point (2, 1, 3) tangent to the plane containing the vector function s(u)=<u^2+2, -u+1, 2u^2-u+3>, find the equation of the... more
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05/22/13

How many 1 kiloton bombs?
How many 1 kiloton bombs would need to be exploded to produce 3.86x10^26 Joules, the amount of energy emitted by the Sun in 1 second?
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