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Chapter 6 Solutions
Calculus and Its Applications (11th Edition)
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- Let u and v be u = [3,0,3] and v = [1, 1, 4]. Verify that: |u x vl? = |u|?|v|? – (u · v)? (c)arrow_forward[. 17. Let aj = 4 az = and b = For what -2 h value(s) of h is b in the plane spanned by aj and a,?arrow_forwardLet u = h = -2 Q---0 4 V= -3 and w= 1 For what value of h is w in the plane spanned by u and v? 7 1 -2 4 harrow_forward
- Q.1. The set of all positive real numbers with the operations x + y = xy kx = xk Is it a vector space? Justify your answer.arrow_forwardLet R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies. u(-9, 5) = -2 v(-9, 5) Vs(-9, 5) V(-9, 5) G,(-2, 3) : 3 Us(-9, 5) = 6 -4 = -1 = 4 G,(-2, 3) (s '6–)'n = -6 = -7 Find R,(-9, 5) and R,(-9, 5). R(-9, 5) R;(-9, 5) Need Heln? Read Itarrow_forwardLet V = span{e2", xe2ª , x²e2¤}. (a) Show that d dx + agze?r + аҙӕ*е2) € V for any aj, az, aҙ € R, (b) Let 0 and represent the functions e2a, xe2* and x²e2x. respectively. For example, 4 represents 3e2 + 4xe2a + 5x²e2ª. 5 Find the matrix of differentiation as a linear transformation on V.arrow_forward
- Use the change of variables X1 X2 X3 X4 = = G(r, 01, 02, 03) : = to compute the content of the 4-ball r cos 0₁ cos 0₂ cos 03 r sin 0₁ cos 0₂ cos 03 r sin 0₂ cos 03 r sin 03 T = {(x₁, x2, x3, x4) | x² + x² + x² + x² ≤a²}.arrow_forwardLet R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies. v(-4, 7) = -8 u(-4, 7) = 4 us(-4, 7) = -5 v₂(-4, 7) = 5 u(-4, 7) = -2 G₁(4, -8) = 8 Find R₂(-4, 7) and R₂(-4, 7). R(-4, 7) = R₁(-4, 7) = Need Help? Submit Answer Read It V₂(-4, 7) = -1 G (4, -8) = -6 Home Copyright © 1998-2023 Carrow_forwardWrite it in detail please.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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