408CF07Assign8Sol - M408C Fall 2007 Assignment 8 Due...

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Unformatted text preview: M408C Fall 2007 Assignment 8 Due Thursday, November 3 You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. l. The base of a solid is the region bounded by the curves y : x2 and y = 4. Find the volume of the solid given that cross sections perpendicular to the y axis are equilateral triangles. 2. Let R be the region bounded by the lines y = m, y : 2x, and y = 4. Find the volume of the solid obtained by rotating R about the line y : 4. 3 a: sin :1? i. " l’ "H '“d'ff‘ t't" tfidtl d "t" f ' = 3 Use ogaii min 1 eren 1a 1011 o 11 1e erivaiveo fix) (1—COSI)($2+1) 4. Find the integrals: da‘ ((1) /;L‘(ln;r)'2' d'r. ) 4 1 (bl/1 M1 + W5 WW Alt) :5 444 W (A, a WW mp$$~7$€dvfiv Aim .5444 mu 6; a M W55 mm. (W5sz in (95x91) +LL Wmmmh WWI; 2/LL dU/Mw— 4mm 1w wt hm Mug—A; ,30 R:4—)c, 77-4 mmw rad/{war 'HL‘ Mot M 33:4} 4v 3=J¢ k R‘”"’ 30 A,{X)=7TRL«TH'L V I = 7T(9—y)‘_7r/q-zx)‘ Yzq,z~f. :W£IL'?X+YL_(IO')‘XWL) ='/’(§ X-3xz'> So r: 4—2yl = 7T(IL ~8Y H1) Th vim mu 94M :3 2 V: J T{3X-3XZ)JX +j4T(/é»8x+xz) Jy o 2. z : ITEZfXL‘xB/L +fiZ/GK'4XL+éx3‘(¥ 2. :77 [—16-9] 4n L éq—£4+ is" - (32~Ia+‘73):{ : 37T 4 thgé—Ie] :7T(§+37$) > gin— MS); S 3 !’—-‘3,—‘”"“ r 5 U1 ' lockuv XW‘V -(YW¥\ (L-CosxVx‘H) ' (I~M¥){Xz+l) 1mm = 3Mm?)+m(Mx3-M(n-wm-sz4,)j 16“ m) = :[wmz mwm)4m(.-m>-xznw>] jp,¢f4,g\,m%‘&tt {Wk/(«A443 w/rL M's/Lu} 407C ,' I 3 - 3 . :5 £60: % . é(—i+loli)c—WV +23! (l—Cosx)(x‘u) hwsv E, 4 (‘0 .2“; 7((lbnx)L w MJMw MAM: 31cm :7 ...
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408CF07Assign8Sol - M408C Fall 2007 Assignment 8 Due...

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