- :-- r-... r-... .'\. 1\ "'\ Math 125 HW 1B Ass ign m e nt Respon ses/j ast? ( 4/3/2 014 JO:57 A. Need Help?

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1 Math 15 HW 1B Ass ig m e t Respo ses/j ast? ( WebAssig Math 15 HW_IB (Homework) Curret Score: - / 60 Due: Moda, April :00 PM PDT Doald Marshall Math 15 Sprig 014, sectio A, Sprig 014 Istructor: Doald Marshall 1. -/10 poits SCalcET Cosider the followig. 4 - :-- r Y = / (x) r-... "' "'\.'\. 1\ \ x (a) Use six rectagles to fid estimates of each tpe for the area uder the give graph of f from x = 0 to x = 6. (i) Sample poits are left edpoits. L6 = I I (ii) Sample poits are right edpoits. R6 =I I (iii) Sample poits are midpoits. M6 = I I (b) Is L6 a uderestimate or of the true area? uderestimate (c) Is R6 a uderestimate or of the true area? uderestimate (d) Which of the umbers gives the best estimate? M6 I of6 4// 014 JO:57 A

2 Math 15 HW I B Assigmet -Resposes/last?d.... -/10 poits SCalcET7 S.1.00.MI. (a) Estimate the area uder the graph of f(x) = 4 cos (x) from x = 0 to x = rr/ usig four approximatig rectagles ad right edpoits. (Roud our aswers to four decimal places.) R4= L~ Sketch the graph ad the rectagles. 4 f (X l = 4 CUS(.I) fix) - 4 (05(X) ~ rl, ,l, ~~~ L. X ~------~~ ~ , ~ ~ +;, ~------~ ~ X fix) = -I C SIX) X 7. ~ :; ". :r " X Is our estimate a uderestimate or a? uderestimate (b) Repeat part (a) usig left edpoits. L4 = I I Sketch the graph ad the rectagles. of6 4//014 10:57 AM

3 Math 15 HW IB /(X) = 4 Cfl"( X ) [(x) := 4. CllS{.) 1. r. ~------~~L L------~~ ~ L~ x X - " H H 8, B 4 [ (X ) = 4 C() S(x) lex) = " co SIX) ~ L ~'------~~'~------~~ X To.T x Is our estimate a uderestimate or a? uderestimate 0f6 4//014 [0:57 A M

4 Math 15 HW 18 eb/stu de t/ass igm et -Res poses/\ast? d / 10 poits SCalcET7 S.l.01.MI. The speed of a ruer icreased steadil durig the first three secods of a ra ce. Her speed at half-secod itervals is give i the table. Fid lower ad upper estimates for the distace that she traveled durig these three secods. Ift (smaller value) :===~I ft (larger value) t (s) v (ft/s) / 5 poits SCal cet7 S Ml. Whe we estimate distaces from velocit data, it is sometimes ecessar to use times to' t, t, t,... that are ot equall 1 spaced. We ca still estimate distaces usig the time periods M, = t, - t, _ l' For example, a space shuttle was lauched o a missio, the purpose of which was to istall a ew motor i a satellite. The table provided gives the velocit data for the shuttle betwee liftoff ad the jettisoig of the solid rocket boosters. Use these data to estimate the height, h, above Earth's surface of the space shuttle, 6 secods after liftoff. (Give the upper approximatio available from the data.) h = I 1ft Evet Time (s) Velocit (ft/s) Lauch 0 0 Begi roll maeuver Ed roll maeuver Throttle to 89% 0 44 Throttle to 67% 74 Throttle to 104% Maximum damic pressure Solid rocket booster separatio f6 4//01410:57 AM

5 Math 15 HW IB Ass igmet -Resposes/last?d ( 5 poits SCalcET The velocit graph of a brakig car is show. Use it to estimate the distace traveled b the car while the brakes are applied. (Use M6 to get the most precise estimate.) I Ift v (fr/ s) 50 I\c 40 ~ '" 0 " " --r t (seco ds) 6. -/5 poits SCalcETl Use the Defiitio to fid a expressio for the area uder the graph of f as a limit. Do ot evaluate the limit. lim, ~ool-t f(x) = x + \( 1 + x, 7 ~ x ~ / 5 poits SCalcETl Determie a regio whose area is equal to the give limit. Do ot evaluate the limit. lim "rr irr L~ta~ X ta(x) o [0, ;] ta(x) o [0, rr] ta(x) o [- ;, ; ] ta(x) o lo, ;] x ta(x) o [-!!..!!..] ' 50f6 4//01410:57 AM

6 Math 15 HW IB tudet! Assigm et -Resposes/] ast?d /10 poits SCa lcet (a) Use the followig defiitio to fid a expressio for the area uder the curve = x from 0 to 1 as a limit. The area A of the regio 5 that lies uder the graph of the cotiuous fuctio f is the limit of the sum of the areas of approximatig rectagles: limf0(.!..-). ~ -> i """ = 1 lim"'!"- "-' i = 0 (.) ' A = lim R = lim [f(x1)l\x + f(x )L\x f(x)l\xl. -' ' 1 Jim)? ( -'-). A... i = ' 1 lim~ (.!..-). ~ lim)7: (~). ~ "or" ~oo ~oo (b) Use the followig formula to evaluate the limit i part (a), ,,, + = [ ( + 1) r- j r ,i 60f6 4//01410:57 AM

Areas and Distances. We can easily find areas of certain geometric figures using well-known formulas:

Areas and Distances. We can easily find areas of certain geometric figures using well-known formulas: Areas ad Distaces We ca easily fid areas of certai geometric figures usig well-kow formulas: However, it is t easy to fid the area of a regio with curved sides: METHOD: To evaluate the area of the regio