MATH 115 Midterm: MATH 115 UPenn 115S08
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Math 115 final exam friday may 9, 2008. Find the tangent plane at(x,y,z) = (2,2,1) and find where z-intercept : 2, 2. 2: 1, 3, - 3, 5, 5. Find the minimum of the function f(x,y,z) = x + 4y + 9z on the surface. = 6 , with x > 0, y > 0, z > 0. Minimum : 1, 6, 2, 2 10, 2, 14, 4, 18. The function f(x,y) = x has critical points at (0, 0) and (1, 1). 1: (e2 1, e, e 2. Suppose the letters aabbc in a jar are drawn out one by one. What is the probability that the letters are drawn out in alphabetical order: 1/120, 1/9, 1/72, 4/21, 1/42, 1/30, 2/61, 1/18. A pack of cards contains 12 cards numbered 1 to 12. What is the probability that all the cards drawn are even numbers (i. e. four of the cards 2, 4, 6, 8, 10,
