Find к for the space curve K(t)=☐ (Type an exact answer, using radicals as needed.)

3. Find points at which the mapping defined by f(z) = nz+z^n (n E N) is not conformal.

Determine whether the space curve given by r(t) =t 2, t 2− 2t − 3, t − 3 intersects the x-axis, and if it does, determinewhere.

Sketch the space curve r(t) = ⟨2 sin t, 5t, 2 cos t⟩ and find its length over the given interval [0, π] .

Sketch the space curve r(t) = ⟨4t, −cos t, sin t⟩ and find its length over the given interval [0, 3π/ 2] .

compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path from (1, 1) to (2, 2) to (0, 2).

find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x - 2y)i + (2x - 4y)j C: The circle (x - 2)2 + ( y - 2)2 = 4

The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

Use Green’s theorem to evaluate ∮C(ye2xy−5y)dx+ (xe2xy−2x)dy, where Cis the counterclockwise oriented boundary curve of the square with vertices at(0,0), (0,1), (1,0), and (1.1).

The graph of f(x,y)=y2-x2 on XYZ space has a saddle point (a,b) if... choice: (choose one correct answer) D(a,b)>0 and fxx(a,b)>0  D(a,b)>0 and fxx(a,b)<0  D(a,b)=0  D(a,b)<0