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Chapter 14 Solutions
Calculus: Early Transcendentals, 2nd Edition
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- Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤ z ≤ 4; f(x, y, z) = e¯² Consider the shown work. To = T, = аф де = д (5 cos 0, 5 sin 0, z) = (-5 sin 0, 5 cos 0, 0) do d -(5 cos 0, 5 sin 0, z) = (0,0,1) дz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = 5 cos 0 0 2π 4 [[ f(x, y, 2) ds = [²* ["^ e S (5 cos 0)² + (5 sin 0)² + 0 = e² do dz k 0 = (5 cos 0)i + (5 sin 0)j = 1 Identify the first error in the work shown. /25 (cos² 0 + sin²0) The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. (5 cos 0, 5 sin 0, 0) √25 = 5arrow_forwardEvaluate the surface integral. J y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u sin(v), v), 0sus 6,0 SV SR. [(10) ()-1] Need Help? Read It Watch Itarrow_forwardFind an expression for a unit vector normal to the surface x = 10 sin (v) , y = u, z = 10 cos (v) at the image of a point (u, v) for 0arrow_forwardLocate the centroid x and y of the area. у T 4 m y=4 1/16x² — 8 m Xarrow_forwardWhat is a unit normal to the surface x?y + 2xz = 4 at the point (2, –2, 3) O+3+歌arrow_forwardUse Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e -3y dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1).arrow_forward[.F. F. dr, where C is given by the vector function r(t). JC F(x, y, z) = sin xi + cos y j+xz k r(t) = ti-j+ tk, ostsi Evaluate the line integral Need Help? Submit Answer X Read It Watch Itarrow_forward· Using an explicit parameterization, perform the following complex con- tour integrals: z" dz [n e Z], $ z-1 dz, sin z dz, where the contours are C1 C2 C3 a b1 aarrow_forwardA milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6 ft. Set-up the integral for the force exerted by the milk on one end of the tank when the tank is full. O 129.2 25°(6. (6-y)√6y-y² dy 0 O 1.655° (6-y)√√6y-y²dy O 64.6 (3-y)√√6y-y² dy 129.2 [13-yi√6y-y²dy 64.6arrow_forwardEvaluate the integral below by changing to spherical coordinates. 81 - v2 V 81 - x2 - v2 (x²z + y?z + z³ ) dz dx dy V 81 - y2 V 81 – x2 - y2arrow_forwardFind the surface area of the portion of the cylinder ya + 2² =9 above tne rectangle in the xy plane. where OEXL2 and -35 ys 3 ........ .. ..... . ....arrow_forwardUse Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise. dy, where Cis the triangle with vertices (0, 0), (6, 0), and (0, 12) 3+ y ху 3 In(3 + y) dx ху 3 In(3 + y) dx – 3+ y dy = iarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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