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MATH 122 Exam 3 - Exam Three MATH 122 Winter 2007 NameSO SU...

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Unformatted text preview: Exam Three MATH 122 Winter, 2007 NameSO SU S lug; g Section Show all your work on the exam paper, leginy and in detail, to receive full credit. No Calculators. There are a total of 105 points on this exam. This exam will be graded out of 100 points; hence, there are five bonus points on this exam. 3 1. (15 points) Find the exact arc length of the curve y = %x3 over the interval [3 , 8]. 5 /,<6 C \1» $13" (k4 __ f \ L 1 3‘ (5*) '" \Xfl “<46 G J? 3/ J —— Z: L . W a 3X U:\L+\ ddcé»! 0655.33 0653?“ 2. (15 points) Suppose that a population of bacteria grows exponentially, and it growth is modeled by the equation y = 600e%° where t is in minutes. Find the average number of bacteria in the first two hours. b _ S ._\_~ g; Ag Zhrs =— \1O mm . Que \9—(3‘ J Cufi 5 o ono\ ' l om)“ O Page 2 of 7 3. (10 points) Find the work required to compress a spring four fifths of a meter if the spring has a constant of 500 Nm“. Hint: F(x) = kx. K; Sam \\I /m \: (fl -=» Ems? W ‘3 X7, fl w—PBFMM : EBQBXb Page 3 of 7 Soéu '— VK) - &U 4. (10 points each) Evaluate the integrals Note: you do not need to simplify your Ixsm(2;)dx -:‘:. -" \ACOSX —¥ SCO5X AV. d0:— dY T. —§<C.OS\A 1 SMX + L (xv f, 3m u ~ \I a -- CD 3X {WW V t X \\\ 6:5} *5 QVL U -=— \<_\ (>3 5 WWW ,._ WMWWMWW do —: .L. 435:3 Aye : ‘X VG?) ’ 5* "V 9 X3 \w‘flm‘ww .. W do _’ éfi‘ éN 7— é¥ \/ 2-. x Page 4 of 7 5. (10 points each) Evaluate the integrals Note: you do not need to simplify your answers. jJ1+cos0sin9d9 k) <— \+ C038 Sxfl—L © an© Jsin30d6 =— J C S \ _ C0329) §\(\éj U: CoSé ‘éUiSWEéfi-D ’5 ,3w®m= ;«v+© _. 3 M/fl— ._ 2:033 ’ cos 9 T L Page 6 of 7 6. (15 points) Evaluate the integral. Note: you do not need to simplify your answer. 2;: 33:61: “’9‘ :2 K 7—»? + 3x 41. fl J x (3‘55) (we?) 2* + 3x -' \1. A (3 C ‘—:. ————-——~ + —-—--~ 4’ —--— X (mxw 1) “A *3 “1 ZXL +3» ‘\1 t A»? - A»: vng -~+ th~+1l5y + CY? “ECX Z: A-t-K‘S-t—L fi‘L—«i—rfiS-eL-fi @-=~—<; 3 —_ _;\+2\3—3<, a 31' *ZQ’EL “\13-‘GA ‘7 A32. +5cvga /> Ci," 6"\ 'L {vyfi\ fix fie; 21 T3 —-\Z, w \ Si, S11- -— J— Zw * 3w— Page 7 of 7 ...
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