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Math 213-001 Assignment # 2 -Sample answers
 

Summary: Math 213-001
Assignment # 2 - Sample answers
1. Compute the requested derivative, first by carrying out the vector op-
eration and differentiating the resulting vector or scalar, and then using
differentiation rules.
(a) r(t) = ti - 3t3k, u(t) = -i + sin(t)k; (d/dt)[r(t) u(t)];
(b) r(t) = et
i + 2t, f(t) = 4t3
; (d/dt)[f(t)r(t)].
Answer.
(a) r(t) u(t) = -t - 3t3
sin(t); then
(r u) (t) = -1 - (9t2
sin(t) + 3t3
cos(t)).
r (t) = i - 9t2k and u (t) = cos(t)k. Using the rules,
d
dt
(r(t) u(t)) = r (t) u(t) + r(t) u (t)
= (i - 9t2k) (-i + sin(t)k)

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics