Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

(b) If u=1, v=2, w>0 . a.hyperboloid of one sheet b. hyperbolic paraboloid c.ell

ID: 2861106 • Letter: #

Question

(b) If u=1, v=2, w>0 .

a.hyperboloid of one sheet

b. hyperbolic paraboloid

c.ellipsoid

d. elliptic paraboloid

e.hyperboloid of two sheets

f.cone

Incorrect: Your answer is incorrect. I choose B

These questions also refer to the mathematica demonstration on page 1060:

Surfaces and Gradients from the Wolfram Demonstrations Project by Nevin Raj.

(a) Fix numbers u=u0, v=v0 and w=w0 If w0=f(x0,y0,z0), then the following statements are true of the gradient vector f(x0,y0,z0) in relation to the plane tangent to the graph of

w0=f(x,y,z) at the point (x0,y0,z0),

a.is tangent

b.is orthogonal

c.points in the direction in which there is no change

d.points in the direction in which f has the maximum rate of change

e.points in the direction in which f has the minimum rate of change

f.none of these

g.all of these

Explanation / Answer

       if u = -1    and    v = 2 and    w > 0

   then    it    will   be    a    hyperboloid    of     one sheet

          Here , w > 0   

            So    Among   all    the     options   , Option A   is   correct

             Hence , Option    A    is    correct