Problem #7:Evaluate the surface integral F.ds whereSF(x, y) = xyi - y²2j - 8-k and S is the sphere²+²+²9 with outward orientation.

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Answered: Problem #7: Evaluate the surface…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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4. Find parametric equations of the line tangent to the surface z = y² + x³y at the point (2,1,9) whose projection on the xy-plane is parallel to the x-axix.
Find an equation of the tangent plane at P = 2,3, 3/e) to the given surface. 4x² + z² ex-x = 25 (Express numbers in exact form. Use symbolic notation and fractions where needed. Let f(x, y, z) and give the equation in terms of x, y, and z.) Incorrect equation: (x-2)(16-e6)e³ + (y−3) (eº)e³ + (z−e³) (2e4) = 0
5. Consider the surface z = f(x, y) = ln (√2³ - y² + 3 cos (2x+y)+7) (a) Find parametric equations for the normal line to the surface at the point P(1, -2, 20). (b) Sketch the normal line to the surface at the point P(1, -2, 20).
Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y – 10)² = 1 in the xy-plane, oriented clockwise? ScF. dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SoF. dr = 0 (d) Now let C be the half circle - (x − 15)² + (y − 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. -0 Lc F. dr =
Let F = (3z + 3x²) i+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F = 0 (b) What does your answer to part (a) tell you about SF. dr where C is the circle (x − 15)² + (y – 10)² = 1 in the xy-plane, oriented - clockwise? SoF. dr = 0 (c) If C is any closed curve, what can you say about La F. dr? SF. dr = 0 (d) Now let C be the half circle - (x − 15)² + (y − 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF·dr = 0
1. Which of the following equations correctly describes the shaded area of the y plane? 6 (A) 2x-y6 3)
I do not understand how they got that answer.
4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1 surface x + 6. and the plane x+2y- 3z =1 at the point (1,3,2). 2
Please solve it more quickly.
Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 25 and z = 5xy. (Use symbolic notation and fractions where needed. Use hyperbolic cosine for parametrization x variable.) x(t) = 5 cos (ht) Incorrect y(t) = Incorrect z(t) = Incorrect 5 sin (ht) (125 sin(h (2t))) 2
2. Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces S₁: x²+y² + z² = 30 and S2: z = x² + y² at the point (1,2,5).
1. Consider the surface x² + y² - 2xy-x+3y-z = 0 at the point Po(2, –3, 14). Determine the following: (a) the equation of the tangent plane to the surface at Po (b) the symmetric equations of the normal line to the surface at Po

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Problem #7: Evaluate the surface integral F.ds where S F(x, y) = xyi - y²2j - 8-k and S is the sphere ²+²+²9 with outward orientation.