Converting to Polar Coordinates:
In Exercises 29–-32, use polar coordinates to set up and evaluate the double
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- www Find the circulation of F = -yi + x²j + zk around the oriented boundary of the part of the paraboloid z = 9 - x² - y² lying above the xy-plane and having the normal vector pointing upward.arrow_forwardUse polar coordinates to graph the conics in Exercises 44–51.44. r = 2/1 + 3 cos θ 45. r = 2/1 − 3 cos θ 46. r = 2/1 + cos θ 47. r = 5/1 + cos θarrow_forwardLet u = u(x, y), and let (r, 0) be polar coordinates. Verify the re- lation |V? = u; + zuổ Hint: Compute the right-hand side by expressing ug and u, in terms of Ux and u y.arrow_forward
- Q. Let f(z)= u(xy)+ Ż V(Z>Y) be analytic function and Z= re Find the Cauchy-Reimann equations in polar Coordinates ?arrow_forwardCalculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to the given x and y axes. r(mm)=144 h(mm)=300arrow_forwardal text I 81 Compute the area of the region enclosed by the polar coordinate equation r = 2 - sin(0). A 1 I DELLarrow_forward
- Exercise x-t+1 Given the parametric equation of (d): (t E R) y = 3 And a Cartesian equation of line (d'): x+3y-0. a) Show that A(2,3) belongs to (d) and O(0,0) belongs to (d'). b) Determine N a normal vector of (d') and V a direction vector of (d') c) Write the parametric equation of (d'). d) Determine Va a direction vector of (d) and N, a normal vector of (D) e) Write the Cartesian standard equation of (d).arrow_forwardDo and b just firstlyarrow_forwardVector 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_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage