Question

(1 point) The figure shows level curves of a function $f(x, y)$. (a) Draw gradient vectors at P and Q. Is $\nabla f(P)$ longer than, shorter than, or the same length as $\nabla f(Q)$? shorter than (b) If C is the line segment from P to Q, then $\int_C \nabla f \cdot d\vec{r} =$ (c) If C is any piecewise-smooth path from P to T to Q, then $\int_C \nabla f \cdot d\vec{r} =$ (d) If C is any piecewise-smooth path from S to P, then $\int_C \nabla f \cdot d\vec{r} =$ (e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then $\int_C \nabla f \cdot d\vec{r} =$ Note: You can earn partial credit on this problem.

          (1 point)
The figure shows level curves of a function $f(x, y)$.
(a) Draw gradient vectors at P and Q. Is $\nabla f(P)$ longer
than, shorter than, or the same length as $\nabla f(Q)$?
shorter than
(b) If C is the line segment from P to Q, then
$\int_C \nabla f \cdot d\vec{r} =$
(c) If C is any piecewise-smooth path from P to T to Q,
then
$\int_C \nabla f \cdot d\vec{r} =$
(d) If C is any piecewise-smooth path from S to P, then
$\int_C \nabla f \cdot d\vec{r} =$
(e) If C is any piecewise-smooth closed path from P to
Q to T to S to P, then
$\int_C \nabla f \cdot d\vec{r} =$
Note: You can earn partial credit on this problem.

(1 point)
The figure shows level curves of a function f(x, y).
(a) Draw gradient vectors at P and Q. Is ∇ f(P) longer
than, shorter than, or the same length as ∇ f(Q)?
shorter than
(b) If C is the line segment from P to Q, then
∇ f · dr⃗ =
(c) If C is any piecewise-smooth path from P to T to Q,
then
∇ f · dr⃗ =
(d) If C is any piecewise-smooth path from S to P, then
∇ f · dr⃗ =
(e) If C is any piecewise-smooth closed path from P to
Q to T to S to P, then
∇ f · dr⃗ =
Note: You can earn partial credit on this problem.

Added by Susan J.

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