Converting to Polar Coordinates:
In Exercises 29–32, use polar coordinates to set up and evaluate the double
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EBK MULTIVARIABLE CALCULUS
- A particle is moving in the plane, so its coordinates ï and y are functions of ₺, and its polar coordinates r and ℗ also are functions of t. At a time when x = -4 and y = 3, and dx/dt = 2 and dy/dt = 1, what is de/dt?arrow_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_forwardRepresent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(0, 0, 0), Q(4, 2, 4) r(t) = %3D Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)arrow_forward
- Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane bounded by the circles x? + y² = 1 and x2 + y² = 4. ww MMMMarrow_forwardV = 6y – 16x + 9z + V¢ Find the curl of vector V in Cartesian coordinates, o is Continuously differentiable. Find: V x Varrow_forwarda) Find the value(s) of (1+ i)2/3. b) Show that cos² z + sin? z = 1, for all z = x + iy, , y E R, V-I= i. c) Find a complex valued analytic function f(x, y) = u(x, y) + iv(x, y), whose real part u(x, y) = 213 – 3r?y – 6xy? + y°.arrow_forward
- Use polar coordinates to evaluate the double integral 2 1 – 2² (1+ x2 + y²)² dy dr.arrow_forwardLet F = Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (6,0,0), (0,6,0), and (0,0,6), oriented counterclockwise as viewed from above.arrow_forwardQ. Let f(z)= u(xy)+ Ż V(Z>Y) be analytic function and Z= re Find the Cauchy-Reimann equations in polar Coordinates ?arrow_forward
- I need a 3d sketch of the equation Z=x+xsiny+xyarrow_forwardDisplacement d→1 is in the yz plane 62.8 o from the positive direction of the y axis, has a positive z component, and has a magnitude of 5.10 m. Displacement d→2 is in the xz plane 37.0 o from the positive direction of the x axis, has a positive z component, and has magnitude 0.900 m. What are (a) d→1⋅d→2 , (b) the x component of d→1×d→2 , (c) the y component of d→1×d→2 , (d) the z component of d→1×d→2 , and (e) the angle between d→1 and d→2 ?arrow_forwardSketch the D indicated and integrate f(x, y) over D using polar coordinates. f(x, y) = 2xy, x≥0, y≥0, x² + y² < 16 Answer:arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage