3 Convert the following equation from Cartesian coordinates

Last updated: 1/9/2024

3 Convert the following equation from Cartesian coordinates to Polar coordinates x 4 y 5 41 a r 10r sin 8 8rcos 0 b 7 Brsin 8 10r cos 0 41 8rsin 10rcos 80 10r sin 80 Br cos 0 0 c d e r 10rsin 8 8rcos 8 41 4 Let f x y x 2 Find f x y cos 3x 2y 2xsin 3x 2y x y x y cos 3x 2y 2x sin 3x 2y x x 3 x y cos 3x 2y 2x sin x 2y x y 3 a a b c d e 3 x y cos 3x 2y 2x sin 3x 2y x y x y cos 3x 2y sin x 2 x x2 5 Given f x y 3x y3 2xy Find the critical points and classify them a 0 0 is a saddle point is a local maximum point b 0 0 is a local maximum point is a local minimum point c 0 0 is a saddle point is a local minimum point d 0 0 is a local maximum point is a saddle point e 0 0 is a local minimum point is a saddle point 6 Which of the following integral do we get if we interchange the order of integration Sony dydx f x y dxdy b fff x y dxdy c fff x y dxdy d ff x y dxdy e fff x y dxdy S SVEY