Question

please i need help in all three this is the second time i post this so please help and do it right this time and show all the work

Sketch the graph of the polar curve r=3 for OSOS 4x and indicate the orientation. Set up an integral to determine how long the curve is, is unrolled (10 pts.] 6. Graph the polar equations r-Sco) and = 3 col) for #/2515./2. Label any key points needed to find the area that lies in the common interior of the two show the setup of any equation needed and you should use technology to solve the equation and find any intersection points. Set up the integral(s) and show all steps to integrate and evaluate manually to find the area. (10 pts] 7. Show all steps to integrate and evaluate manually to find the arclength. [10 pts.) 8.(a) Show all calculus to determine whether the sequence (A.) - - (3) converges or diverges. (b) Show how to find a formula for the sequence of partial sums (S.) for the 2 Infinite sum and use limits to find the sum of the infinite Σ 7° +5n+6 series.

Answer 1

2 Ir-50sso La < CH2 g. 3 Cayo 5C,30 = 3 Casa 73(4G, 50-9690) 3610 9) 20 Corpo - 155690 – 3 Coso o 7 20 Ca 30 18 Casoro or 2010 (10 Cas?6-9) =0 2 Cororo on 10 Cas20 90 2 = 0/2, © = G5" (W) talo 2 So, the area = S (5590)–(30p)}] 2 - = fas Cosso do y la bodo 6 25 -xa Cos? 30 do - 2 x 2.5 Ca?o do ( fra den finden ato arbe 1+Gs CC do -75, 1764920 do 2 M fin 60 [ot fin2o 10% ] [ 04 Se noge 2 CS ed wimScanner

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ya 2 Ave length 3² + (3. lns)? yo lov V got 900 (en)? do q (1+(299) 9 +0 44 Viffen3)2 10 ua - Vit (en)? vit 843)? 3 do 2 -7.99 en 3 - Vit (en3)? 49 en 3 199 1+ an We know =e. my eb alow, An It 6 lim (+ 2)?") 6 nyd Csoned camScanner

*** (col-), 5 Σ natsuts 2 + 2 t 1?tsite 2²+5.2to Take its nth partial Sum n²tsnto Sua 2 1245-146 +- 2 t 22+5.246 + 2. n't shts sh 2 ky k²t5k to - Lely brea 2 k = 2 buk k²tiskt 6 2k? k24skto 1 k2 акт 2. Kits + 2 when lim k2 k to its at lim bu ky Its/ut u 2 #1 Sency { bn is cal- so, {an is cyl- .( 2 2 Taking Sun kt (k+2)(x+5) I *²5k46 ka -2E Kt2 ka Kth CS

Sn = 2 not Mt2 nota 215-****$ths ac is into) Sna lim Sn = 2 hayo (****) uti 18 2(%) = 213 = 42 n²tsuto 2 na CScanned with CamScanner