math_172_(fall_2008)_(schumaker)_second_exam_(spring08)

# math_172_(fall_2008)_(schumaker)_second_exam_(spring08) -...

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Math 172: Second Semester Calculus Spring Semester, 2008 Second Exam # 1 2 3 4 5 6 Total worth 15 15 20 15 14 21 100 score Name: Section: ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. ( 15 points ) Let C be the curve (shown below) defined by x x y , cos . Write down, but do not evaluate , an integral that is equal to the arclength of C. C

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Question 2. ( 15 points ) An industrial-strength spring, obeying Hookes’ Law F ( x ) = kx , has a natural length of 1 meter. It takes 300 Joules of work to stretch the spring from 2 meter to 3 meters. Find the spring constant k and the amount of force F (in Newtons) required to hold the spring at 2 meters. k = _____________ F = _______________ 1 m 2 m ? Newtons natural length
Question 3. ( 20 points ) Solve the differential equation x y dx dy sin 3 , subject to the initial

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Unformatted text preview: condition . 1 ) ( y Question 4. ( 15 points ) Consider the geometric series: 4 1 3 n n (a) Give the first term and the common ratio. (b) List the first four terms of the sequence of partial sums . (c) Determine the value of the series or show that it diverges. Question 5. ( 7 points each ) Consider the following series of positive terms. Use an appropriate test to determine whether they converge or diverge (a) 1 3 / 2 2 ) ( sin 1 n n n (b) 2 2 1 n n n Question 6. ( 7 points each ) Determine, with justification, whether each of the following series is absolutely convergent, conditionally convergent, or divergent. (a) 1 2 2 ) 1 9 ( n n n n (b) 1 1 . 1 1 ) 1 ( n n n (c) 1 2 2 n n n...
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## This note was uploaded on 02/14/2011 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

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math_172_(fall_2008)_(schumaker)_second_exam_(spring08) -...

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