Suppose that l lines are drawn through a circle and these lines form p points of intersection (involving exactly two lines at each intersection). how many regions r are formed inside the circle by these lines? assume that the lines end at the edge of the circle at 2l distinct points.

Find the local maximum and minimum values and saddle point(s) of the function. if you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function 5. f(x, y) xy y + y 6. f(x, y)-xy 2x 2y x-y 7. f(x, y) x-y)1 - xy) 8. f(x, y)y(e- ) 9. f(x, y)-x y* + 2xy 10. f(x, y) 2 x* + 2x? - y? 11. f(x, у) — х* — зк + 3ку? 12. f(x, y)xy3 - 3x2 - 3y2 - 9x 13. f(x, y) — х* — 2х? + у? — зу 14. f(х, у) — у сos x 15. f(x, y)e cos y 16. f(x, y)xye-lw? +y2\/2_ 17. f(x, y)xy e° 18. f(x, y)(x2y')e 19. f(x, y)y2 2y cos x, -1 7 20. f(x, y)sin x sin y, -