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1 Let R = ln(u2 v2 w2), u = x 2y, v = 2x − y, and w = 2xy Use the Chain Rule to find ∂R ∂x and ∂R ∂y when x = y = 1 Solution The Chain Rule gives ∂R ∂x = ∂R ∂u ∂u ∂x ∂R ∂v ∂v ∂x ∂R ∂w ∂w ∂x = 2u u2 v 2w ×1 2v u v 2w ×2 2w u v w2 ×(2y) When x = y = 1, we have u = 3, v = 1, and w = 2, so ∂R ∂x = 6 14 ×1 2 14 ×2 4 14 ×2 = 18 14 = 9 7 ∂R. F a Ă d ݂̌ł ɂ ĉ b ێ a l ĊȒp ɓ ̂ w f 鎖 ł ܂ b. A t h l e t i c D i r e c t o r s s i m p l y n e e d t o c l e ar l y c o m m u n i c at e w i t.
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P = F·v P = vermogen (Js1 of W) F = kracht (N) v = snelheid (ms1) Kinetische energie E k = ½m·v 2 E k = kinetische energie (J) m = massa (kg) v = snelheid (m/s) Zwaarteenergie E z = m·g·h E z = zwaarteenergie (J) m = massa (kg) g = 9,81 m/s 2 (op aarde) h = hoogte (m) Veerenergie E v = ½C·u 2 E v = veerenergie (J) C = veerconstante (N/m) u =uitrekking (m) Chemische energie E ch = r V ·V E ch = r. As ˚respects scalar multiplication As is the inverse of ˚it follows that (rw) = rv= r (w) Thus respects scalar multiplication Hence is linear Lemma 1211 Let V and W be isomorphic vector spaces If one of V and W is nite dimensional then they are both nite. 5 h v s r q v d e loh g h ood v w u x w w x u d r u j d q l d w ly d 6 h u y l lr 6 lv w h p l, q i r u p d w ly lh 7 h oh p d w lf l 3 4 k / dd/s/ / ed 7 lw r or ' h v f u l lr q h 7 ls r $ lr q h 5 lt x d oli lf d lr q.
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