MATH 105 Midterm: MATH 105 2005 Winter Test 2
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Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal di culty. (a) assume that z(x, y) is a linear function with slope 2 in the x-direction and slope 3 in the y-direction. If z(1, 1) = 4, nd z( 2, 1). If f (x, y) = ln(x2 + y), nd lim k 0 f (1 + k, 0) f (1, 0) k. Answer: (c) let (x0, y0) be a critical point of f (x, y) = x2 y2 + 6x + 8y 21. Find (x0, y0) and then nd the equation of the tangent plane to the surface f (x, y) at the point (cid:1)x0, y0, f (x0, y0)(cid:2). Answer: (d) suppose the marginal revenue in producing x units of a certain product is. Find the change in total revenue if production is increased from.
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