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- 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+ 2 sin 0 at the points (–1,3) and (2,5). .At which of the following polar coordinates is/are the tangent line(s), on the polar curve T = eº, vertical? Select one or more: (e-3π/4,-3) (e/4, 4) (3, e³/4) (,e/4) None h (e³/4, 3) (e-/4,-1) (-7, e-/4) (-3, e-3/4)
- Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z). Q4] A complex function in term of polar coordinates, (r, ) is described as f(z)=u(r,0)+j v(r,0). The Cauchy-Riemann equations in polar coordinates are 1 dv ar ди dv 1ди %3D r d0 ar And the Laplace equation in polar equation in polar coordinates is 1 a2ø r or ' r2 a02 1 дФ %3D ar2 By employing these equations, show that Ø(r,0)=°cos(20) is harmonic and obtain harmonic conjugate, v(r,0) of u(r,0). The auxiliary of the harmonic conjugate is v (0,0) =0. HUAWEI Nova 2 Plus DUAL CAMERALet R(r, theta) = (r*cos(theta))er (polar coordinates) How do I find v (velocity) for r = 2, theta = pi/4, dtheta/dt = 2, and dr/dt = 3?Consider the family of curves described by the parametric equations x = a cos t + h, y = b sint + k. (0 ≤ t < 2π) where a ≠ 0and b ≠ 0. Describe the curves in this family if (a) h and k are fixed but a and b can vary (b) a and b are fixed but h and k can vary (c) a = 1and b = 1, but h and k vary so that h= k + 1.
- 3, Evaluate LL -2 J-√4-x² by using polar coordinates. (4- y²) dydxRecall the polar form of the Cauchy-Riemann Equations: 1 ƏV 1 ƏU r +0. r d0 av ar dr -i0 (0 + i). Let f(z) = z45. Use av dr The derivative can be recovered by f'(z) : the polar form of C-R equations to prove that f has a derivative at all non-zero points and show that f'(z) = 45z44. = e ar7. Let f(z) = . Use the polar form of the Cauchy-Riemann equations to determine where f is differentiable.