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Math112-exam1

# Math112-exam1 - Math 112 EXAM I February 19 2UC3 Read each...

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Unformatted text preview: Math 112 EXAM I, February 19, 2UC3 Read each problem carefully. Show all ycur wcrk ltr ea(h problem! No Calenlatere! 1. [10) Evaluate the follcwingintegrale: (a) / 2(73+1)1/3a7:' (1) [ﬂag— 2. [10) Find the length cf the curve .7: : 35(92 + 25/2 ever 0 g y g 3. 3. (10) Find the area cf the surface of revcluticn generated by revclving the curve y : .713, 0 g .7: S 1, about the .7:-axis. 4, (15) Evaluate the follcwing limits: 5 332 ar—Cl‘lsligéi)’ (6) mag;— a (() li_m(1+51)1/173 (a) ling 5. [20) Find? mfor the follcw1r1gfur1et10r1c (a) y =10g464'”, (b) y = 71-”, (C) y = aldanﬁcswﬁl): (a) y = (1 + 2‘1)?“- 6. [15) Evaluate the follcwing integrals: (a) [6.31% (a) full—ad“; 1 F 1 n 1 4— (c) /0 \/1 — vmam. (Hint: suhEt1tute u = 1 — v.7) 7. (10) A tank has the shape of the surface generated by rctating arcurd tlce y—axis tlce graph of y : 2.7:, O 3 .7: 3 l. The tank is initially ﬁill Cf water WllCl] weighs 62.5 lh/t'tsr‘. How much work is done in pumping all the water to the level cf the tep cf the tark? 8 (a) (5) Evaluate the follcwing limit lim _ 1 Hm 7:]r17:' (b) (.5) Determine the ecnetant, (,3 given the fellcwirg: (.7:+1-”’ Ilirn —>00 (.7:— 1 ...
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