Use a graphing utility to sketch each of the following vector-valued functions:
28.
[
T
]
r
(
t
)
=
〈
e
cos
(
3
t
)
,
e
−
sin
(
t
)
〉
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.
Find the directional derivative of the function at the point P in the direction of
the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, the
point P, and the unit vector u.
1. f(x,y) = x² + y², P(1, - 2), 0 = .
Find the directional derivative of the function at the point Pin the direction of
the unit vector u = cos ei + sin 0j. Sketch each the graph of the function, the
point P, and the unit vector u.
3. f(x, y) = 3x – 4xy + 9y, P(1, 2), v = i +j.
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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