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Sample Final

Sample Final - Full Name MATH 122 Sample Final Exam Section...

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Full Name: Section: MATH 122: Sample Final Exam Thursday, December 10, 2009 Show all work and justify your answers. Your solutions should read nicely and be legible. They should not be composed of regurgitated fragments of your mind scattered throughout the page. If you run out of room for a problem on the front, then continue onto the back. Remember no calculators are allowed. 1. (a) Find the length of the curve defined parametrically by x = t and y = ln | cos( t ) | for 0 t π / 4. [12 pts] (b) Find all points of horizontal tangency on the curve defined parametrically by x = 3 t 1 + t 3 , y = 3 t 2 1 + t 3 . [13 pts]

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2. (a) Evaluate 4 x 2 + 1 x 4 dx [15 pts] (b) Evaluate 6 t ( t 4)( t + 2) dt [10 pts]
3. (a) Determine if the integral 2 1 t 2 + 4 t + 8 dt converges or diverges. If it converges deter- mine the value to which it converges. [15 pts] (b) Use the error formula for Simpson’s Rule to find the smallest number of subintervals necessary to approximate ln(2) = 2 1 1 x dx with an error less than 10 6 . Phrase your answer as “let n be the least number of (even?) subintervals greater than . . . ” [10 pts]

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4.
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Sample Final - Full Name MATH 122 Sample Final Exam Section...

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