APPM 2350 Final: appm2350spring2017examfinal_sol

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turquoisegnu128

31 Jan 2019

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1. (a) a parameterization of the bug"s path is r(t) = cos 2t i + sin 2t j with velocity vector v = r (t) = 2 sin 2t i + 2 cos 2t j and kvk = kr (t)k = 2. Thus t(t) = r (t)/kr (t)k = sin 2t i + cos 2t j. When t = 0 the bug is at the point (1, 0) implying that t(0) = j. (b) t = e2y i + 2xe2y j = t (1, 0) = i + 2 j. Thus (c) dt dt dt ds ds dt. = (2 c/cm) (2 cm/sec) = 4 c/sec dt ds (cid:12)(cid:12)(cid:12)(cid:12)(1,0) = t (1, 0) u = (i + 2 j) j = 2 c/cm. (d) the most rapid rate of temperature decrease will occur in the direction of t . At (1, 0) this will be i 2j. (a) integration region in the xy-plane consisting of two sets of hyperbolas.

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APPM 2350 Final: appm2350spring2017examfinal_sol

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Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

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