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

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

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...

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

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...

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...

For the plane curve r(t)=ti+(lncost)j+0k Determine T(t):

Let g(x,y)=(xy)^(1/3). e.Does the graph of g have a tangent plane at (0,0)? Explain briefly. f.Is g differentiable at (0,0)? Explain briefly. I asked this question yesterday...

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

Length is independent of parametrization: To illustrate that the length of a smooth space curve does not depend on the parametrization you use to compute it, calculate the length of one turn of the...

A formula for the curvature of a parametrized plane curve a. Show that the curvature of a smooth curve r(t) = f(t)i + g(t)j defined by twice-differentiable functions x = f(t) and y = g(t)...

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...

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

Set up an iterated integral to evaluate I=R⌠⌠⌠f(x,y,z) dv, where R is the region in the first octant bounded by the surface z=x+y^2, the cylinders y=2sqrt(x), x=2sqrt(y), and the xy-plane The...

i have no idea solving the problem :((

a. Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 4 + 3 cos t, y = 4 + 3 sin t, pi/2 ≤ t ≤ 3pi/2 b. Describe the motion of...

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