Question

Polar Coordinate Problems 1. Identify when the function decreases when changing r2sin (29) = a(-1]b to coordinates Cartesian a = 1, b = 5 2. Draw the polar curve given byr = a (b + c cos (@)) in 0 s@sx/2. Find the arc length of that curve. a = 1, b = 5,C=-7 Sequences and series. For series, identify the method or technique to be used before applying it. If you are going to use root criterion, reason criterion, alternating series criterion, comparison criterion (justify the comparison), series p (justify indicating converge or diverge according to the value of p), serious geometric (justify indicating converge or diverges according to the value of r), criterion of divergence, criterion of the integral (verify that the hypothesis is fulfilled), limit comparison criterion (indicate why it converges or diverges or both) 148 is a sequence increasing, decreasing or 1. a.) Determine if the sequence not monotonous when = 1, b=5 b.) Determine if this bounded. c.) Determine if you converge, justify 2. Determine if the sequence on converges or diverges. 3. Determine if the sequence converges or not. If converges, find the sum g 1, b5, de-3 .. 15 Ptos) 1(a/b) b. (10 Pros) Žmon+d) c. [10 Pton] Ža**** 4. Determine if it converges or diverges. If it is alternating and convergent, determine if it converges conditionally or absolutely. A=1, b=5, -7, d--3 . pros 5.17 Post EP PO Ś**+*+1 4. pyron - 15 WiWiWi .. peros Como 1. Jy mong let one

Answer 1

I Let an Q-bn a Tum when a = 1 6=5 then an = 1-5n Itn a) Now anti- An = 1-5(n+!?. ?-51 to +1) (+) | 1-50-5 na 1-50 Itn - 6-59-4)(1+n) - 6-sn)(n+8) (M+1)(n+2) (sn + Shop +4 +4n) - (m+d=58#lon) (n+1)(n+8) -Shatu + a-gn-sha - (+12 +) -6 to V MEN (n + 1)(n+a) =) Anti -an to k neno VNEN - Anti Tan te a > As > G3 au 29s ? --- a sequence can here is a monotoricaly dceraning sequence Key

6) smie Ons het om ice therefore a, = 4 =-2 which is upper bound of sequence con) (u it in mountainly dorang sequence) and lower bound of sequence be -5. KI - sequence can man io Source (-) Yes (and or in convergent and its limit point is / " (annal is both monotonic and l bounded therefore it must be convergent COY nico mo itn. nuo Hence (and is convergent Sequence and Converges to us.