Exam_exam_2_ - MATH 241 2nd Examination Prof Jonathan...

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MATH 241, 2nd Examination Prof. Jonathan Rosenberg Friday, October 28, 2005 Instructions. Answer each question on a separate answer sheet . Show all your work. Be sure your name, section number, and problem number are on each answer sheet, and that you have copied and signed the honor pledge on the first answer sheet. The point value of each problem is indicated. The exam is worth a total of 100 points. In problems with multiple parts, whether the parts are related or not, the parts are graded independently of one another. Be sure to go on to subsequent parts even if there is some part you cannot do. Please leave answers such as 5 2 in terms of radicals and do not convert to decimals . You are allowed use of a non-programmable calculator and one sheet of notes. 1. (25 points, divided as indicated) (a) (15 points) Find the tangent plane to the surface x sin y cos z + e xy + z 2 = 1 at the point (1 , 0 , 0) . (b) (10 points) Is it possible to locally solve for z as a smooth function of x and y (in a neighborhood of (1 , 0) ), and if so, what are
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