MATH 215 Midterm: exam2f04
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Do not submit loose sheets of paper they won"t be graded. Some useful trigonometric identities: sin2 + cos2 = 1 sin2 = 2 cos 2 = cos2 sin2 cos2 = 2 sin 2 = 2 sin cos x = cos( ) sin( ) y = sin( ) sin( ) z = cos( ) This problem is about the iterated double integral. Y/2 y exp(x5) dx dy (a) sketch the region of integration and change the order of integration. On your sketch give the equations of the boundary curves and please circle your answers. (b) evaluate i by computing the double integral of your answer to part (a). Problem 2. (a) using the method of lagrange multipliers, nd the area of the largest rectangle with pairs of sides parallel to the coordinate axes that can be inscribed in the ellipse x2 + 4y2 = 1. Also give the coordinates of the corner of the rectangle in the rst quadrant.
