math1120_sample_prelim1

math1120_sample_prelim1 - Find the area between the curves...

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Math 1120: Prelim I (September 29, 2009) Your Name: Your Instructor’s name: Your Lecture Number and/or Day and Time: This exam has 8 pages with 6 problems adding up to 100 points. If you need extra space, you can use the other side of each page. No calculators or books are allowed – you may have one 8.5 x 11 formula sheet. Please show all of your work (including the intermediate steps). Writing clearly and legibly will improve your chances of receiving the maximum credit that your solution deserves. Good luck! Problem # Max pts Earned 1 20 2 15 3 15 4 18 5 18 6 14 Total 100 Academic Integrity is expected of all students of Cornell University at all times, whether in presence or absence of members of the faculty. Understanding this, I declare I shall not give, use, or receive unauthorized aid in this examination. Signature of the Student: 1
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Problem 1. Evaluate the following expressions: (a) (5pts) d dt Z 6 t - 5 t - 7 e x 2 dx = (b) (5pts) Z 1 0 ( d dx [(2 x ) (2 x ) ]) dx = 2
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(c) (5pts) Z 2 x cos( x 2 ) dx = (d) (5pts) Z x 5 x 3 + 1 dx = 3
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Problem 2. (15pts)
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Unformatted text preview: Find the area between the curves y = 6 x 2 and y = 12-6 x for ≤ x ≤ 2. 4 Problem 3. (15pts) The region bounded by y = sin x + cos x , y = 0, x = 0, and x = π/ 2 is revolved about the x-axis to generate a solid. Find the volume of this solid. 5 Problem 4. (18pts) Find the length of the curve defined parametrically by x ( t ) = t 2 y ( t ) = 1 3 t 3-t ≤ t ≤ 2 . 6 Problem 5. (18pts) The curve y = √ 2 x + 1 from x = 1 to x = 7 / 2 is revolved about the x-axis to generate a surface. Find the area of this surface. 7 Problem 6. A cake is formed by revolving the below shaded quarter of the disk ( x-1) 2 + y 2 ≤ 1 about the y-axis. (a) (7pts) Set up but DO NOT EVALUATE the integral that would compute the volume of the cake using WASHERS . (b) (7pts) Set up but DO NOT EVALUATE the integral that would compute the volume of the cake using CYLINDRICAL SHELLS . 8...
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This note was uploaded on 12/06/2010 for the course MATH 1120 taught by Professor Gross during the Fall '06 term at Cornell.

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math1120_sample_prelim1 - Find the area between the curves...

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