Concept explainers
Verifying Stokes’ Theorem Verify that the line
9. F = 〈y – z, z – x, x – y〉; S is the cap of the sphere x2 + y2 + z2 = 16 above the plane
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Chapter 17 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- 4. Consider the vector function r(z, y) (r, y, r2 +2y"). (a) Re-write this vector function as surface function in the form f(1,y). (b) Describe and draw the shape of the surface function using contour lines and algebraic analysis as needed. Explain the contour shapes in all three orthogonal directions and explain and label all intercepts as needed. (c) Consider the contour of the surface function on the plane z= for this contour in vector form. 0. Write the general equationarrow_forwardPlease show all work!arrow_forwardFind a parametrization of the surface z = 3x² + 8xy and use it to find the tangent plane at x = 1, y = 0, z = 3. (Use symbolic notation and fractions where needed.) z =arrow_forward
- Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector normal to the surface S. Determine F as well as the area of the plane perpendicular to F if surface S = 2xy + 3z.arrow_forwardHow do you do this?arrow_forwardsketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function using the given parameter. Surface: x2+y2=4; z=x2 Parameter: x=2sin(t)arrow_forward
- Use Stokes' Theorem to find the work done on a particle moves along the line segments from the origin to the points (2,0,0) (2,4,3) , (0,4,3). and back to the origin. Note that this (counterclockwise) path is a rectangle on the plane z = 3/4 y. The motion is under the influence of the force field F = z2 i+ 2xy j + 4y2 karrow_forwardYour friends correctly calculate the gradient vector for f(x, y)=x+y° at the point (2,-3) as follows: Vf(2,–3)=(2x, 2y ) =(4.-6) %3D (3.-4) They say that (4,-6) is orthogonal to the surface at the point where x=2 and y=-3 (at the point (2,-3, 13)). Unfortunately, they are incorrect, and you will help them. (a) For f(x, y)=x² +y² ,what is (4,-6) orthogonal to when r=2 and y=-3? (Drawing a picture may help) %3D |arrow_forwardUse Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) F. dr where F = (x + 6z)i + (8x + y)j + (10y −z) k_and C is the curvearrow_forward
- c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x=2, x=-2, y=0 and y=4arrow_forwardin both ways of stokes theorm, thank youarrow_forwardLet S be the surface described by the vector function Ř(u, v) = (v², u + v, eu). Find an equation of the plane tangent to S at the point (4, -2, 1).arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning