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Math 2321 Quiz 3
September 24-25, 2020
Name
1) (3 points) You are given the position vector p = p(t), in meters, of a particle at time t seconds.
Determine the position, velocity, speed, and acceleration of the particle at the given time t0 seconds.
p(t) = (t2 , t4 ), t0 = 1. Be sure to include units.
2) (2 points) You are given the position p = p(t) of an object in Rn at time t. Find the distance traveled
by the object between the given times t0 and t1 . p(t) = (t3/2 , t), t0 = 0, t1 = 20/3.
3) (2 points) Determine the gradient vector function of q(x, y) = x3 y − 4x2 y 2 + xy 3 .
4) (3 points) Suppose that f (x, y) = x3 y −5x2 y 2 +2xy 3 and that you are given that f (−1, 3) = −102 and
∇f (−1, 3) = (153, −85). a) find the linearization of f at (−1, 3), (b) give an equation for the tangent
plane to the graph of f at (−1, 3, −102), and (c) use the linearization to estimate the value of f at
(−0.999, 2.997).