رو V レス Question 4 dx2 0=30° 11 tan O tan 30° COS =2. Find the radius of curvature [15] (a) Given a = 1 + sin 0, y = sin 0-cos 20, d²y dx2 show that and the coordinates of the centre of curvature for the point on this curve where 0 = 30°. (b) Find the range of values of x for which the following series is absolutely convergent X x2 2:3 24 x5 2 x 5 + 3 x 52 4 x 53 + 5 x 54 + 6 x 55 Question 5 (a) If V = In(x² + y²). Prove that -743²)-2x( (x²+y2)2 a²v av + = 0. მე2 Jy2 [10] [15] 2. Jy 27 Jx (b) Find the sum of the series 242-202 2(x²+2)-2y(24) 2x2 x²-2y2 (x²+y2)² 8 1+2" n=1 3n-1 Jaz 4 буг [10] - 2y²-2x² 2x²=2yz 2 +-