MATH 0240 Midterm: MATH 240 Midterm 1-59
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This test consists of 10 problems, each worth 10 points. All work must be shown in order to get credit. Please write legibly and explain your logic by words whenever appropriate. Consider the points a(0, 0, 0), b(1, 0, 1), c(1, 2, 1). Find the equation of the plane tangent to the surface z2 2x2y + xyz + 5 = 0 at the point (1, 2, 1). Find the linearization l(x, y) of the function f (x, y) = 3 sin( (x2 + y2)) + 4 at the point (1, 2). Find the maximum rate of change of f (x, y) = x3y2 3x + 2 at the point (1, 2) and the direction in which it occurs. Assume that the equation xey + y sin z + zex = 0 de nes implicitly z as a function of x and y. Find or show that the limit does not exist. lim (x,y) (0,0) f (x, y)