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Verify Formula (1) in the Divergence Theorem by evaluating the surface
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Chapter 15 Solutions
EBK CALCULUS EARLY TRANSCENDENTALS SING
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- 6. Use the Stokes theorem to evaluate f Fdr where F (3x – 2y +32) i +(4x – 2y+32) 5 + (2x – 3y | 22) k and C is the circle: æ = 3, y? | 22 = 4, oricnted counterclockwisc when vicwcd from the positive part of x-axis. Describe the surface S whose boundary is C and state its orientation.arrow_forwardDetermine the point(s) on the surface z = e(3x² +9y2) at which the tangent plane is parallel to the xy-plane. (Use symbolic notation and fractions where needed. Give your answer as a comma-separated list of coordinate points of the form (*, *, *).) (x, y, z) = Incorrect 0,0,0arrow_forwardAnswer it as soon as possiblearrow_forward
- Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3, center at (2, 0, 0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0, 0, 0). Find the flux of curl(F) across S and then evaluate the circulation & F. dr. (Use symbolic notation and fractions where needed.) DS Incorrect JC curl(F). dS = F. dr = 18T Incorrect 18Aarrow_forwardUse Stoke's Theorem to evaluate the line integral -4ydx +-3zdy+dz where C is the intersection of ralf-4 the xy -plane and hemisphere z = √1-x² - y² traversed counterclockwise viewed from the top-that is, from the positive z-axis toward the xy-plane.arrow_forwardLet F =. Compute the flux of curl(F) through the surface z = 1- x² - y² for x² + y² ≤ 11 oriented with an upward-pointing normal. Flux = help (fractions) (Use symbolic notation and fractions where needed.) Hint: Stokes' Theorem shows a direct computation can be done in an alternative fashion.arrow_forward
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