x=4(sin^2)tcost y=4sin(cos^2)t

x=4(sin^2)tcost y=4sin(cos^2)t

We know that the curvature of the helix r(t) = (a cos t)i + (a sin t)j + btk (a and b are equal or greater than 0) to be K = a/(a^2 + b^2). What is the largest value K can have for a given...

Find all of the extrema of g(x,y,z)=xyz on the surface z=e^(-x^2-y^2).

How would I trace this on the xy and yz coordinate plane as as well as the planes y=±4

Describe the region bounded by the planes: x = 0, y=0, z=0, x+y=4, and x=z-y-1. Describe as a region (in any order you can) the region inside the ball x^2+y^2+z^2=4 and...

Evaluate ffD(x^2+y^2)dA where D is the region in the first quadrant bounded by y=x, y=3x, and xy=3

Lagrange multipliers work great for finding the minimum value of y-ax, restricted to the curve y^2-x^2=1 for any a with 0<=a<1 (what is it?) but fails quite miserably if a >=1. Use the geometry...

Find the extrema of f subject to the given conditions. f(x,y,z) = x+ y + z x^2-y^2=1 2x+z=1

For each vector field in R4 given below, either find a function for which it is the gradient, or explain why no such function exists. Variables are in the order x, y, z, w. a.(siny +...

Let F(x,y)=3x^2yi+(x^3+y^3)j. By integrating, find a function f so that F=del f. Don't forget your constants of integration!

Show that the path x(t)=(cos(t-1),t^3-1,1/t-2) is tangent to the surface x^3+y^3+z^3-xyz=0 when t=1

The curvature K is defined as k=||dT(s)/(ds)|| Use the chain rule to show that k can be expressed as: k=||T'(t)|| ...

Show that |x|^2 = (x · a)^2 + (x · b)^2 + (x · c)^2 calculus 3 regarding to vectors

Suppose that x^2+y^3-z^4=1 and z^3+zx+xy=3. a.Take the total differential of both these surfaces. b.The two given surfaces intersect in a curve along which y is a function of x...

Use differentials to find the approximate amount of copper used in the four sides and bottom of a rectangular copper tank that is 6 feet long, 4 feet wide and 3 feet deep inside if the sheet of copper...

The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1 Intersectto form a curvilinear quadrilateral R. The change of variable u=y-x^2, v=y-(x-2)^2 map R onto a square in the uv-plane. Use the...

Let g(x,y)=(xy)^(1/3). a. Is g continuous at (0,0)? I put down yes since it's not undefined there. b.Calculate ∂g/∂x and ∂g/∂y when xy≠0. This wasn't too bad and...

Here's the question: Find the most general function f:R^2 --> R such that ∇f(p)=p for each p∈R^2. So, I'm guessing this means that I just need to find a function of x and y...

Is f(x,y)=sqrt(x^2+y^2) differentiable at (0,0)? Justify. I don't think the partial derivatives exist due to the limit definition, so can I say that the function isn't differentiable...

If f(t)= ⌠1/t (1/x)ln(tx) dx 1/T⌡ where...