Suppose that r t is a smooth vector -valued function of t with r ' 1 = 3 , − 3 , − 1 , and let r 1 t be defined by the equation r 1 t = r 2 cos t . Then r' 1 π / 3 = ________ .
Suppose that r t is a smooth vector -valued function of t with r ' 1 = 3 , − 3 , − 1 , and let r 1 t be defined by the equation r 1 t = r 2 cos t . Then r' 1 π / 3 = ________ .
Suppose that
r
t
is a smooth vector-valued function of t with
r
'
1
=
3
,
−
3
,
−
1
,
and let
r
1
t
be defined by the equation
r
1
t
=
r
2
cos
t
.
Then
r'
1
π
/
3
=
________
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in
the direction towards P₂(5,4,2).
əz
Ju
əv
B- If Z = 4e* Iny, x = In(u cosv) and y = u sinv find and
4.
) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7)
in the direction of the unit vector ū = −²¹+]
√5
Suppose that the temperature T at point (x, y, z) is given by
T(x, y, z) = sin(xyz)
and that an insect currently at the point (5, 0, 8) moves slightly in the direction parallel to the
positive y-axis.
As a result, the bug will feel the temperature...
decrease
stay the same
increase
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