4.1 - MA 160 Section 4.1 Worksheet Name G CL r a 0 in The...

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Unformatted text preview: MA 160 Section 4.1 Worksheet Name G CL r- a +0 in The Area Under 3 Graph The formula for the area of a trapezoid is A = 2.5051 + b2). Use this formula for problems 1 and 2 below. ”2 1. Total cost from marginal cost. Photo Shop has found that the cost per card of producing x note cards is given by 60:) = —0.04x + 85 for x s 1000, where c(x) is the cost in cents per card. Find the total cost of producing 650 cards. Find the area of the shaded region to get the answer. Clan-.- 95M MA MW“ (0, £5). C-(éifi'o) =-" -—-o‘4(é:5'0\+95' :— *&@+95=5?Aa few-poo}: 4:6 (£25035?) W=Miamz=t§hCb;+h1\=i(cso)(95+5¢) : 395(19‘4) : ‘fé,<?ao W : Hégda-eQac/L 2. Total profit from marginal profit. A company has a marginal profit function of P'(x) = —2x + 85 , where P’(x) is in dollars per unit. Find the total profit from the production and sale of the first 40 units. Make a sketch showing the appropriate area. We) = 95M FYI/a): - 2(4Ial+?5': .— 20 “95:5 Acme. Jaw W M (0)85)M(4o,5')c 0AM, :- TMW: gums»): {.1403 (amiss 1"- QG(?G‘) :.. £1300 Marginal Pmfil (3 per unit} 3. Approximate the area under the given graph of f (x) = x2 over the interval [1, 71 by computing the height of each rectangle, finding the sum of the heights, and using the formula given below. Calculate height -' m} of rectangle using . ‘ . . ' t:+:0:¢ .53.! .34.; * '" O O 0 9393-1. I' 1 . 0:. .' - To? For this problem, each rectangle has assigned a width of 1. The variable x; represents the left endpoint of each subinterval that will be used to calculate the height of the ith rectangle. . Complete the table at right. Notice for this .1 "14 5 5 problem the last it value in the table is 6 since the last subinterval is from 6 to 7. 0.}: G O o 0 . 3‘: . U‘. R“: k. . . :0:.:.'. . O O '0'. 0‘ O . O I :.:.;.;.;.;.:.;. O I Q C 0 1.5.0’. 9‘. 9 '5] C 0......LU. . . . . . v v .. 0. 0+. 0 0 a. o u to D For each Riemann sum problem, the area is found by using the formula , area = {width} times (sum of heights). 3 , ...- b "Q— ___,_ ’7" k _ This is symbolized as area: Ax-Zf(x,.). m’ A k "‘ w "' 4: : 4:» f l i=1 Now completethis problem: Area: Ax-me) = I ' (if : Cf! i=1 x1 used to Calculate calculate height of 4. Approximate the area under the following graph of C (x) r: x over the interval [1, 7] by using rectangle width of K. Compute the height of each rectangle, find the sum of the heights, and use the formula. The variable Xi represents the left endpoint of each subinterval that will be used to 59 F93 calculate the height of the ith rectangle. Complete the table at right. Notice for this probiem, there are 12 its and x1 is 1 and x1; is 6.5. W:Au= b‘Q/Yi;.é. :. H ”r is). l 4.. 1:"; Answer: l Area = moifbri.) =3—(éta‘15') i=1 sum of heights = from =__._._4 0”" 5' ii '6 2° 1; U] Reimann Sum Problems on the Calculator Reimann sum problems can be worked on the calculator using the STAT key. On your calculator go to STAT, EDIT and input the x; values in L1. Then move the cursor to the top of the next column labeled L2. Press enter and the cursor will move to the bottom of the screen so that you can input the formula for the function. For exampie, for problem 4, input L12 so that each value of column 1 is squared and put in column 2. Then go to the home screen and input (1/ 2) *sum( L2) to get the answer of 102.25. The sum operator is located at 2"”, STAT which goes to LIST. Go across to the MATH menu and select S:sum(. li-IHMES DPS m Here is the screen containing the MATH menu. Emnt To get sum( , go to 2"d STAT = LIST, g; $235.; go to the MATH menu and select S:sum(. 4: "Ed ' 3W: Press ENTER to paste sum{ in the home screen. 1933:“: ?~istdfleu ( 5. Use a calculator to do the following problems. Approximate the area under the graph of fix) over the indicated interval with the given number of subintervals. Use b-a n decimal places. For each part of problem 5 draw the rectangles on the given graph. Wag: width of rectangle = Ax = for the interval Ea, b] and n is the number of rectangles. Round each answer to 6 1 3' .f(x)= x2 I [ZISL n = 3 X! :9. x :3 5—; .. 3 3“ Ax=b""= 3 ”—3774 ”3;? n AnswerSa: Area: Ax-sum(|_2) = i" (o ‘123 é ”Hi i) Wfiédr 10-4236” J, Answer: Area = Ax- sum(L2) = 9' (’7’ 11$ 3 6 “<9"? .3.) 1 5C. f(x 3—2 , [2,5], fl =12 __l__, Answer: Area: fix-sumuz) : ‘i (L 30 6W5- 9oéé’) : 0.3976‘é5 Wééip. 5d. Approximate the area under the graph of f(x) = 0.13:3 + 1.2.1::z — 0.4x — 4.8 over the é interval E -10, 4] usingj’subintervals. v — an— —m a .2. ; Ax=b a = __ 4, f n ‘—“‘"—""_— Answer5d: Area: Ax-sumle) z I (“1“”) 33122.7 6. Express 25: —2 i without using summation notation. Simplifyyouranswer. l. D :(‘QV4 (“AV-a- (‘21)1-e C-;)3+ (-;)q+ (-9.); ‘:.. I wa+qv9+ibvgg —""— _,_..—-.-. .._.—— 7. Write in summation notation: 5+10+15+20+25+30+35 = S'ri+5’-a_+§.3+§“f+5-5+S’-(§.*5‘-7 : ’7 Z 5.; «L : l Answers: 1. 46,800 cents or $468 2. $1,800 3. 91 4. 102.25 51). 0.357313 56. 0.327465 5d. 3:233:54 6. -21 {5162/7 5a. 0.423611 7. 23:15:' ...
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