Writing a Tangent PlaneIn Exercises 57 and 58, show that the tangent plane to the quadric at the point
Ellipsoid:
Tangent Plane:
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Calculus
- Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = (x - y) i + (x + y) j; C is the triangle with vertices at (0, 0), (7, 0), and (0, 6) a) 0 b) 252 c) 84 d) 42arrow_forwardFlux across hemispheres and paraboloids Let S be the hemispherex2 + y2 + z2 = a2, for z ≥ 0, and let T be the paraboloid z = a - (x2 + y2)/a, for z ≥ 0, where a > 0. Assume the surfaces have outward normal vectors.a. Verify that S and T have the same base (x2 + y2 ≤ a2) and thesame high point (0, 0, a).b. Which surface has the greater area?c. Show that the flux of the radial field F = ⟨x, y, z⟩ across S is 2πa3.d. Show that the flux of the radial field F = ⟨x, y, z⟩ across T is 3πa3/2.arrow_forwardFinding Curvature In Exercises 23-28, find the curvature of the plane curve at the given value of the parameter. r(t)=(t, sent) , t=pi/2arrow_forward
- Calculus In Exercises 43-46, let f and g be functions in the vector space C[a,b] with inner product f,g=abf(x)g(x)dx. Let f(x)=x+2 and g(x)=15x8 be vectors in C[0,1]. aFind f,g. bFind 4f,g. cFind f. dOrthonormalize the set B={f,g}.arrow_forwardFinding Inner Product, Length, and Distance In Exercises 35-38, find a p,q, b p, c q, and d d(p,q)for the polynomials in P2using the inner product p,q=a0b0+a1b1+a2b2. p(x)=1+x2, q(x)=1x2arrow_forwardFinding Inner Product, Length, and DistanceIn Exercises 17-26, find a u,v, b u, c v, and d d(u,v) for the given inner product defined on Rn. u=(0,7,2), v=(9,3,2), u,v=uvarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning