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Calc III Ch13 Notes_Part17

# Calc III Ch13 Notes_Part17 - u Z4i><>5rmm Aw 0 KW...

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Unformatted text preview: u Z4i><>5rmm Aw 0 KW? m .ﬂﬂﬂ/M XIV 6142an Q! m9: 0' ' ﬁﬁ ” 13g — Directional Derivatives and radients) We saw how partial derivatives gave the slope when moving in the x-direction and y— direction. What if we re mOvin'g in yin: ' ' Let u —- a b) be the, t vector in dthe desired direction. Then D ﬂx, y)— '- ﬂ ()4 +_ A Uv'f VeCfurz‘ ' NOTE: The booklike to use €=cos.9i+sin6i, so Duf(x,y)= (056 3C; + SING g3 See text for formal deﬁnition. Ex: Find Duf(x, y) if f(x,y) = x3 —3xy + 4y2 and u is given by6 = 7r / 6. FindDuf(1,2).= u.- @505 H,’ Ins/NF“. I/ E .- Z 43"__ L +_Z_ 7,! ~ 3x - 3/ ’ - J /= 'ZX + 3 + y V f 00%“? :[3XZ'_3&>+2’:’5< +in @ 0; Z Find Du f (x, y) if f (x, y) = xy and the directional vector v starts at P(2, 3) and L K stops at Q(4, 2). ———> FindDuf(2,3). PQ :42. / , l > um“ at???" ; «(é ; 3; :L new we «re; 1 G K W- ...
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