The figure shows level curves of a function f(x,y).
(a) Draw gradient vectors at Q and T. Is gradf(Q) longer than, shorter than, or the same length
as gradf(T) ?
(b) If C is the line segment from P to Q, then
int_C gradf*dvec(r)=
(c) If C is any piecewise-smooth path from P to T to Q, then
int_C gradf*dvec(r)=
(d) If C is any piecewise-smooth path from S to P, then
int_C gradf*dvec(r)=
(e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then
int_C gradf*dvec(r)=
The figure shows level curves of a function f(, y).
as V f(T)?shorter than
(bIf C is the line segment from P to Q,then
7f .dr=
cIf C is any piecewise-smooth path from P to T to Q,then
Vf.dr=
30
d) If C is any piecewise-smooth path from S to P, then Vf .dr =
2
3
(Click on graph to enlarge)
e If C is any piecewise-smooth closed path from P to Q to T to S to P,then
Vf.dr=