(a) Let F = x3yi + 2xz3j + (z3 + 4x2)k . Computecurl F (1, 2, 1).(b) Consider the family
Chapter 20, Problem 50(choose chapter or problem)
(a) Let F = x3yi + 2xz3j + (z3 + 4x2)k . Computecurl F (1, 2, 1).(b) Consider the family of curves Ca given, for 0 t 2, byr (t) =i + (2 + a cos t)j + (1 + a sin t)k .Evaluate the line integralCa F dr and computethe limitlima0Ca F dra2 .(c) Repeat part (b) for the family Da given, for 0 t 2, byr (t) = (1 + a sin t)i + 2j + (1 + a cos t)k .(d) Repeat part (b) for the family Ea given, for 0 t 2, byr (t) = (1 + a cos t)i + (2 + a sin t)j + k .(e) Compare your answers to parts (b)-(d) with part (a)and explain using the geometric definition of curl.
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