MATH 120 SPRING 2008 WEEK 13 RECITATION
(1) Plot the gradient vector fields and level curves of the functions given below:
(a)
f
(
x, y
) =
x
2

y
2
(b)
f
(
x, y
) = +
p
x
2
+
y
2
(2) Evaluate
Z
C
xy
2
ds
where
C
is given by
r
(
t
) = (cos
t, t,
sin
t
).
(3) Evaluate
Z
C
xydx
+
ydy
where
C
is the sine curve
y
= sin
x
, 0
≤
x
≤
π/
2.
(4) Let
F
(
x, y
) = (
y,

x
) and
C
be the line
y
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 Spring '10
 Tor
 Math, Vector Calculus, Meaning of life, Line integral, Covariance and contravariance of vectors, Vector field, Gradient

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