Revenue from Two Products A company manufactures and sells two competing products,
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- Another derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued function. a. Take the dot product of F and the del operator; then apply the result to u to show that (F•V )u = (3 a + h az (F-V)u + g + g du + h b. Evaluate (F - V)(ry²z³) at (1, 1, 1), where F = (1, 1, 1).arrow_forwardCalculate the value of fa F · dr, where F = yzî + zaj + xyk C is curve x2 + y2 = 9, and z = y2arrow_forwardaf Let f(x, y, z) = xy + z². Calculate where x = = s², y = 2st, z = t². მsarrow_forward
- 2. Let U be a vector function of position in R³ with continuous second partial deriva- tives. We write (U₁, U2, U3) for the components of U. (a) Show that V (U • U) – Ü × (▼ × Ü) = (U · ▼) Ū, (V where ((UV) U), = U₁ (b) We define the vector function of position, by setting = V × . If the condition V U = 0 holds true, show that ▼ × ((Ū · V) Ű) = (Ũ · V) Ñ - (Ñ· ▼) ū. (Hint: The representation of (UV) U from the first part might be useful.)arrow_forwardNo. 6 (a, b, c)arrow_forwardB- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the direction towards P₂(5,4,2). əz Ju əv B- If Z = 4e* Iny, x = In(u cosv) and y = u sinv find andarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage