In Exercise 69 and 70, find curl
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Chapter 15 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- use surface integrals of vector fieldsarrow_forwardThe flux of the vector field F(x,y,z)=3zk across the closed rectangular box with opposing vertices at (0,0,0) and (6,5,7) is: Using surface integrals, not divergence theorem. Note: Next week we learn a theorem that will make this problem much easier, but for now you need to work out a surface integral and show your work or explain your geometric reasoning.arrow_forwardSketch the graph of G2 in xyz-plane and yz-plane(R) then SET-UP the required triple integral. No need to evaluate.arrow_forward
- Set up integrated integral base is the triangle in the xy-plane bounded by the x-axis and the lines y=x and x=4 and whose top lies in the plane z=6-y.arrow_forwardExplain how to compute the surface integral of a scalar-valued function ƒ over a sphere using a parametric description of the sphere.arrow_forwardb) Use any expample and sketch a condition to prove that the curl of a gradient is zero (0). Briefly explain your answer.arrow_forward
- A particle moves along line segments from the origin to the points (1, 0, 0), (1, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 5xyj + 4y2k. Find the work done.arrow_forwardWhat does it mean if the curl of a vector field is zero throughout a region?arrow_forwardState the theorem for Vector Surface Integral.arrow_forward
- Explain how to compute the surface integral of a scalar-valuedfunction ƒ over a cone using an explicit description of the cone.arrow_forwardA particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .arrow_forwardLet a vector field be given. What is the integral representing the work done by F along a curve C which is the parabola , from (0,0) to (1,1) ?arrow_forward
- 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