Ch5-1WSSol - ’ Mrs Waldron BC Calculus Ch...

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Unformatted text preview: ’ Mrs. Waldron BC Calculus § Ch 5.1 (a) (b) (c) (d) (e) (f) (9) Estimating Area with Finite Sums < Ex 1: A bug begins to crawl up a vertical wire at time t = O. The velocity v (in ‘ inches/sec) of the bug at time t/(in seconds), for 0 5 1‘5 8, is given by the function ' whose graph is shown below. -—g.-__l-_..L--_;-. How far did the bug travel from t = 0 to t = 6? 3+th~ 3 = l; mam What happened exactly at t = 6? M 3+0? Pit-d How far did the bug travel from t = 6 to t = 8? l U161“! dean?) What’s the significance of the fact that part of the graph lies above the x-axis and part lies elow? The P I [4,, a m mpr‘gagt is who kit/«a moves I? . " " we» U “ " “ \g/ How far did the bug travel from t = 0 to t = 8? ' IO meow What is the GEOMETRIC or VISUAL significance of this total distance? _ H13 Cl came) down lmcffi Show how the units of time and velocity are put together so that you end up with the right units for all the HOW FAR questions. d: lth-b ‘3, mm,mcw:r mam ' 826;, l. e mm W537 “mam Rectangular Approximation Method (RAM): w 4W Ex 3: A particle starts at x = 0 and moves along the x-axis with velocity v(t) = t2 for time t a 0. Where is the particle at t = 3: N *9 “if” LRAM: MRAM' 01+ *5“ 5+ em (iv = Hairs": C 2.51., gets/I i : RRAM: ‘ f 2 +12 4' 32"“ /L,‘ Which RAM is the biggest? Smallest? Most accurate? fichy-m AREQM 1% 341% xix) 0,33: Oi m/les+= LEI‘W fiasfacmrw'e’: ”7 KM? g :5 5. Z i, E g. .. "vwvmwv'm , Ex 2: Suppose a car is moving with increasing velocity. We measure the car’s velocity every two seconds, and obtain the data in the table below: Time sec .5- 2 4 6 8 10 Veloci ft/sec m- 30 38 44 48 50 a) Give a lower and upper estimate for how far the car has gone in the first two seconds. power: 202.0} 3 4/0 upper = a '( Bo ) a 60 b) Give a lower and upper estimate for how _far the7car has gone after 10 seconds. How much “3:55:23: Isthhmerfefllgrtgosi (signage: E" + 4 ‘4 +44 8.3 3. 5&0 WW”: 2» £313.34" 38 .+ 9‘9; 4,. Li‘g‘t'fiifi‘l "'3' H520 Plot the 10-second data, and fit it with a smooth curve. Di Rig/anti, =' GO tint: (no) Example 2 continued... Now let’s increase our accuracy and take measurements every second. -_-2345678910 ”-i'l-IZO 26 30 35 38|42 44 46|48|49 50 WW Wmfi’fim a) Give a lower and upper estimate for how .far the car has gone after 10 seconds. How 33???? 95'?" gestured + L/ 2. +49 ,.., twe- r W .,. W =93 era 2‘; 1:» 30 + 3,5» +32 + clam KM «we 4» WM? MazL/og (if? D»; gem—ace. = 30 b) If you took measurements every 1/4 second, what would the difference be between your upper and lower estimates? IS— / a: = m “Mews-mew“ «WWW c) If you wanted your error to be no more than 1/10th of a foot. how often would you have to take measurements? ( l ' A _, A n Qn (.9, = Qn (gm x :2 24'“ < 500) l - _L vh me. = V 6’)“ i 500 ,th ( 2.3 g 226} l , Plot the one—second data, and fit it with a smooth curve: (2:; > 8" 27'? : 3—230 Seam v MW : ”mwwwvw—w—v m. \wm-«TWW «My (it/w) WWWWVWWA‘M. WW7, .ww Npmw m, . _ “.mrwsfl, Approximate Total Distance Traveled for a s t s b g E; E E: ; m Wm“ “WWW “wavy“ .- armr- Ex 3: Estimate the volume of a sphere of radius 4. V"? 2%} WW oil 033M 5% ’2-f1: VOW <54: 3%le ‘9 7 592 T'I’rz‘fi ) h; r=oq q ‘QIT/Z'FZ; Wye—v1) (:0 (=0 [fig/’7 r dW-I-[le + /5‘+ M/f— ¥j= Mew?” XEQH’; CS};}‘:!‘".,€. DEF/‘7‘ f¥+ 0] = 7°77 ...
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