08finsol - 1. Calculate the limits, showing your work. (Do...

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Unformatted text preview: 1. Calculate the limits, showing your work. (Do not use L’Hospital’s Rule.) . 1 1 [In ’94:] (a) 31% 5; Hx(m+2) E10 rm (5) hm GOSH t—‘O sint KL’») £11m BL ., / d1, XKX+1)_-;z;: 9’70 XOc'I—R) ‘ ’ flux-1L2) X “a O 7P) 0 9—7 be m if “’0 w. .6 jean?de 1M1£:O j' Mi 1 Han- 2. Find f’ (2) for 1 max/1” x/t3+1dt. LeAL Agm‘zgijfi €71“ Arm 2 VX3+I “fl-X) 7A (Vb) A” 1 m, :A’W—fl 2120/wi (—41) Ma .2 VWTM) 3. Calculate dy/dgc_ DO p43] (a) y=sec(fifi‘f) [:0 W51 (b) yugzl (0“) 2 Am,W317)mam)(a(xK+1)”£)zgxa) .2 .. ‘1- U) 3 +Xj ~l gcT-jg: +37! +X(—9FQ);L% :0 [93“ :7 _Jfl—{ '( L (a) Calculate 4. Let f(:z:) :2 [x2 -— 1], fosfim)dx. .7 :i h Find the (:bsolute) maximum and minimum of f (m) on the interval [—1 /21 2], s owmg your wor . if) Evy? EIE’CEI N '2 Xl—l X :4, 752: l l 13 .3 J. 3’ (Mg I~XR6140+ X‘Q-l J70 zX—JZ—X zo +3X—x o i I U—é) +(Mr3) "C; --—|)) (lg) iLLhflh—Qx} (xawf)-:9~)C x34; W0 / szm (iii-x: {C(ozom 0,2w WWtJ—J 5. Use the definition of the derivative to show that if f(£E) : x/233—E—3 [mm @792 —~2 [Fm +2) 6. Evaluate the integrals. O (a) fcscsmcotmdx /0 )aa‘gj (b) facsmdx (&)u:(/G~C_x obgdw/CDC MCX MK A70 : 'VZ’Q chax 041,20 (5%):0975 :Jugedwy._3l»uffc : my?“ a (L) :X‘Q»! X23LL+( Amazxe XVZ/Cgéi’u guy-:0 (19):? Q i :2 ‘ i S fut/flirt =5] Xalxtlfwobc I 3 , . . 3 ‘ ~23 (“NFL/{51“ *ij‘ M/Zf/‘l’l—ruéotu O o — Z I. 2 51 55- 3/; : Elihu +3 u o _ 5/ 73/ :{Em “3%) 3‘ 7. Find the intervals on which the function 1 1%th is increasing and decreasing, showing your work. g+x.— X2 : [32“)()U+X) >0 (DI/wovirmrf 3‘X>0 HX>O ~I<X<oz J/ Whig—+an A I 9\‘5/‘1 {(x) : ~—";[2+7(-X) (P8X) .__ Jx— 34x (“JUL-WC”??? 2x470 {f- xwg) Maxi/o :L xc “ 0’“ (A3) 8. Set up, but do not evaluate, definite integrals for the volume of the solid obtained by rotating the portion of the first quadrant bounded by y = 2 —- 3:, y = 3:2 and the y—axis in the manner indicated. 3 (IL; :7 (a) Rotate about the :r—axis. t th ' = _ 3 FA 1 (b) Rotate abou 6 line x 3 61' : -“?C 10 {3] 9. (a) Prove that the equation 3 l) x5/3+2x=coscc has at least one solution. , (b) Prove that the equation 35/3 +2z = 0053: as at most one solution. £00 '7: R’s/3+5}? ~ WK Wifiwwouf . I .57 m- [M Lo) :4 <0, L[7T/Q_}:~(‘V gm )0 .ao M02012] IVT' )0) «[[M :7[(é)‘=0 (/Z’I 7C’(C)::o [W C, L; (659) $3 flaw/uh) 4‘qu ! 751*)25269/3—m4—4m9c a o+&+(r2):)>o '3 11 10. (a) Find the equation of the tangent line to the curve 1; = (x + 1)‘2 at x = a for a > 0. quadrant by the fiam‘s’ the 9'8st and the tangent line to y = (cc + 1)‘2 at a: = a is g j (b) Find the value of a > 0 5110b that the area of the triangle formed in the first a maximum. (You do not have to prove that it is the maximum) ’4 (M : "(WHDTS A” LEE—Z) ": "QICU-I-z) 3 . I X? ._ ‘ MR 2; : Helm-H) 3(X‘f‘ou) —r (Lg—H) '1 [3:9) gLCL+I)f3(X-.. ):((,L+{) g +, l _ CL goes») n+1 V:a%+m— at P —a mu") (77—3(CL+I) 3PM + (0+1) Dia+ (11+!) 5 lg”! (0k+l]3 (Cu—Q3 5—. ‘ .2 ‘ ‘ (Ba—H) OWN»: ( :_L 3Ct+( Sad-I) Z A 0-) AK 9 )((a+l)2 (“JPN-)3 ( iaflf‘flfNZ/Ccflf) Am}: MUM-()9 ~ 2 DWZafljéawr'Ug: /a[3a+()9‘(a+z) RUM!) 7361+} (lama :2 Eat—H azl ...
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08finsol - 1. Calculate the limits, showing your work. (Do...

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