20. Show that the second derivative test is inconclusive when applied to f(r, y) 2 at (0,0). Describe the behavior of the function at the critical point For the next few exercises things to know are: 1. In a closed and bounded region, a continuous function will assume a maximum value and it will assume ImIIm valuic. 2. These values have to be assumed either at a critical interior point or on the boundary. They canot be assumed anywhere else. Maybe I should add a thid thing, if a problem asks for the maxior m VALUE of a function, one might consider that a value is a number, not a pair of numbers or a point in the plane. Any answer that is not a nmber is essentially wrong 21. Find the absolutemaxiuand the absolute miu vles of theution f(x,y)y2-2r 2y on the closed triangle R of vertices (0,0), (2,0) and (0,2) 22. Find the maximu and the mium value of the following function in the indicated domain. If there is no maxIInI or immiII,SaLy so z2 y2l in the closed disc { (z, y) : z уг < 9} /(z, y)-13 2 and y-8 2 23. Compute RxydA: R is the region in the first quadrant bounded by Z-0, y 21. Wf(,y) dA as an iterated integral in the order du dy, where R is the region i quadrants 2 and3 bounded by the semicirele of radius 3 centered at (0,0) 25. Evaluate ITR y2dA where R is the region bounded by y = 1, y = 1 z, y = z 26. Find the volue of the solid in the first octant bounded by the coordinate plans and the surface 27. Sketch the region of integration and evaluate the 28. Find the volue of the solid bouded by the paraboloids z 22 y2 and 27 -2-2y2 29, Sketch the region inside both the cardioid r 1 cos θ and the circle r 1, and find its area. y2 dA where R is the region bounded by y1, y 1-r, y- 1 1y -r2 dy dr by reversing the oder of integration y and -27