Math121FinalSols

# Math121FinalSols - SOLUTIONS TO THE FINAL MATH 121 FALL...

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SOLUTIONS TO THE FINAL MATH 121 – FALL 2003 – KUNIYUKI 126 POINTS TOTAL, BUT 120 POINTS = 100% 1) Approximate the area under the graph of fx x () = 1 from a = 2 to b = 14 by finding a Left Riemann Sum using 4 rectangles of the same width. Round off to four decimal places whenever you need to round off. (14 points) Step 1: Find D x , the width of each rectangle. D x ba n = - = - == 14 2 4 12 4 3 Step 2: Find the left breakpoints. ax xxx æ Æ æ= æ Æ æ Æ +++ 1 3 2 3 3 3 4 2581 1 Step 3: Find the Left Riemann Sum. f x 1 1 2 3 1 5 3 1 8 3 1 11 3 15 06 0 375 0 2727 ◊+ ◊+ () = Ê Ë Á ˆ ¯ ˜() + Ê Ë Á ˆ ¯ Ê Ë Á ˆ ¯ Ê Ë Á ˆ ¯ ˜() ª+ + + = DDD D ... . 2.7477 square units Note: The exact value is closer to 1.9459.

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2) Flubber is consumed at the rate of ft t () = 3 2 tons per year, where t is the number of years since January 1, 2000. How much Flubber is consumed from January 1, 2002 to January 1, 2005? (9 points) 3 52 125 8 2 2 5 3 2 5 33 td t t Ú = [] =() -() =- = 117 tons 3) Find the integrals. Simplify wherever possible. (50 points total) a) xx d x 32 1 5 7 - - Ú cont. on 1,5 12 4 43 44 (8 points) You may write your final answer as a decimal.
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Math121FinalSols - SOLUTIONS TO THE FINAL MATH 121 FALL...

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