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Math 206A Quiz 05 page 1 03/04/2011 Name. Suggested Sluton 1. Suppose that u(x) = ; GG) a) NG), KG) where the fouri component functions fg, h, bere real-valued and x =(z,y,z). Suppose furthermore that 2 = r? +s +t, y = s?t°, and z= e** +r‘, and ni(r, s, t) is the vector-valued function ariel iseoe ccs Gomera tenceareeee paella 1A. Find J(7); simplify all entries. A/C, $, t)= (r? +S Naty SH emir ¥) 2r 35% 1 JAj=| O 2st© See" Ys OO 8e* 1B. how many rows, and columns, does Ju have? rows = [a] columns = [=a 1C. Let uy be uo mi, and let uy be the second component function of uy. Find and simplify to the extent possible a formula for Ouy.2/dt. (Hint: Fill out just enough of Ju so that with your answer to 1A you can find the answer to this problem) Ta [te ond peg heed Jao hho f a “te dy he ft A) Syl" + (8%) cs 2 * z : Whee 4,3 Sand Hp, 7 oll be tnd: Poo ath 2. Let P = (3,4) and Q = (15,9) be two points in the plane. Let f(«,y) = «23+ zy. Let u be a unit vector pointing in the direction from P to Q. 2A. Find the directional derivative of f in the direction u at the point P. Show all your work. Express your final auswer as a decimal to five places after the decimal point. The vecbr fom Pi» @ & (i2,5) ). es lang 6 [it*es* = (3,50 2 init vechor ponky tom P PreQ@eo + r(i2,5), Met OF les a (3x%4, B49 *) [is i (31,2) & haclechonee derives (3], 3) 0 & (72,8) = 75 (392 +15) = BE 124, 76703! 2B. What is the approximation to this partial derivative, using h = 0.1 and the difference quotient (f(P + hu) — f(P))/h? Show all your work to five places after the decimal pone => —_ ——$—$—_——$—— eed Prhi = (34) * oer £ (2,5) = \= (80983 0 KOPEMY ze #(P+h)-£(P) 42,059 — 31 _ 3.057946. h om Ol 
