We consider the vector field F = (xy², -x²y). Let C be the parabola y = = x² from the point (-1, 1) to the point (1,1). Find the work exerted by this force along the curve C.

Q: Find the directional derivative of the scalar field = x¹y + 4xz at the point (2, -2, 4) along the…

A:

Q: Find the positive t when the vector r r(t) = (3t, 4t², 10t² - 4) is perpendicular to r'(t). t =

A:

Q: Find r'(t), r(t), and r'(to) for the given value of to r(t) = (1+t)i + ³j, to = 1 (No Response)…

A: We have to find the values of r't, rt0, r't0 where rt=1+ti^+t3j^, t0=1 and sketch the curve…

Q: Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the…

A:

Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

A:

Q: Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) =…

A: rt=et,e2t,t0=0

Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

A:

Q: Let the velocity vector be v(t) = (6 cos(3t), 8 exp(2t), 3t2). Compute the acceleration vector a(t).

A:

Q: Let 7(t) (-t + 5, 3e , - 5 sin( – 3t)) Find the unit tangent vector T(t) at the point t =0 T(0) --…

A: