Thomas' Calculus: Early Transcendentals

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Unformatted text preview: Name W 5dx l. Evaluate/m. Fem: x3+3~x1+52< = ch‘z-P-Zx-rS). WM M4 Name _____________—_ 2. For each of the following integrals, state Whether it converges or diverges, and give your reasons carefully and clearly. 00 a./-wcos2tdt. wwméae 9‘53“ {'03 Name 3. For each of the following series, state whether it converges or diverges, and give your reasons carefully and clearly. Name 4. Find the Taylor series, centered at —1, of f (2:) = i. I ‘ ’ Name 1/2 3 5. Estimate / 6‘13 dx with an error no bigger than 1/100. Give your reasons. 0 s m. 7, ,{EVW e 2 (4—144-19 +£11.34.” fizwéw—L) ; J W M wWRmu/defl‘ WWW W 6” 9M 3+ch> MIR/x3152." “2% f e 314‘: I: (1—7509 +5‘ (260%: D J, I l : (raw + jimmy 0 0 I I, ’1- ) 1 "L 21; 1. OROCJIX ’L “L I 2 32%, + SfR‘xMx WWQM‘M" £3: 3"” J. ~ ‘ wig—mi ’7 1. __’L__, M L = “fir/o = 2M ) ”’5‘ 'X ‘J” Name 6. Find lim 6 :C—>O fiL' - ‘ a x3 x~ MK ’V lg m. )c —> a ( ‘ )7" 3 2. )c-rAA/wx _ )c £1in WT“ 3 AM (3..) X ~)o ‘3 X‘50 \C 7 Name 7. Find the area between the origin and the curve given in polar coordinates by 7“ z 969 for 0 g 6 3 7r. 7 A: §6w%£110:£v% (989)229 : ELL 92819439, {Vt I= {92819499} 9 “5:91) W: 62 JD 19 @2949) '17: 12' 8 M ) Name 8. Find all roots of 11:6 ~ 3x3 + 9 = 0 in polar form: a: : rei . Name 9. Consider the region under the curve y : e“$ and above the CE-axis for O S m < 00. a. Revolve it around the :c—axis and find the volume. £ 3 -2 - : 11M 5 e ’44! = 77% (‘%€ bllo 3%” ’ tau . - A w ( +a>[email protected] 5m» ' b. Revolve it around the y—axis and find the volume. 0° 6 V: O 19“”, 16') J4 :: Q‘W/Kw. l0 xe‘rfix . law T9 t” ”6'7“,” u=x )ww'ffy 00,049, ~7=-6 )M 5xe"09¢ ~ 3m we w: - e ”C ”W 7‘ }‘ vb \/= QWM (“Xe ‘6‘ ){a Name 10. Find the arc length of the curve given by y = 2:2 for 0 S :c 3 fl. (You may find the formula 6t 9 1 /sec36d6: sec an + E/seceaw 2 U Name 11. The mass m of a crystal in a solution grows at a rate proportional to m2/3. The original mass is 1 gram and the mass after 24 hours is 8 grams, Find the exact value of the mass as a function of time. WLWW ’WLZ/ G M: 3 h a. W ) é) /m(o)=l @ mom-:56, M9” ‘5 3 = .LfluHCB' m 1’7 [email protected] 3 1" 2L’7C 3C3; )M 3 WV 553(317‘4'33. W3) 3 23 3 ._ __ . - ”.1 S; >,2‘:7(h2‘rr3) J 2,—3- (pl‘r+3)) h “if“ ’3’ 3 ...
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