FDWKCalcSM_ch5

FDWKCalcSM_ch5 - 234 Section 5.1 Chapter 5 The Definite...

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234 Section 5.1 Chapter 5 The Definite Integral Section 5.1 Estimating with Finite Sums (pp. 263-273) Exploration 1 Which RAM is the Biggest? 1. LRAM > MRAM > RRAM 2. MRAM > RRAM > LRAM 3. RRAM > MRAM > LRAM, because the heights of the rectangles increase as you move toward the right under an increasing function. 4. LRAM > MRAM > RRAM, because the heights of the rectangles decrease as you move toward the right under a decreasing function. Quick Review 5.1 1. 80 5 400 mph hr mi i = 2. 48 3 144 mph hr i = 3. 10 10 100 ft/sec 2 i sec = 100 ft/sec ft h mph ii 1 5280 3600 1 68 18 . 4. 300 000 3600 1 24 1 365 ,/ s e c km hr hr day days i 1 1 yr yr i ≈× 946 10 12 .k m 5. () ( ) ( ) 6 3 5 2 18 10 28 mph h mph h += + = 6. 20 1200 gal/min 1 h 60 min 1h gal = 7. (( . ) ( −° + ° =−° 11 5 6 3 C/h)(12 h) C h) C 8. 300 1 24 1 25 920 ft /sec 3600 sec h h 1day day 3 i = ,, 0 00 ft 3 9. 350 50 17 500 people/mi mi people 22 i = , 10. 70 3600 1 1 0 7 176 400 times/sec h h times i ., = Section 5.1 Exercises 1. Since v ( t ) = 5 is a strait line, compute the area under the curve. xt v t == = () () ( )() 45 2 0 2. Since vt t =+ 21 creates a trapezoid with the x-axis, compute the area of the curve under the trapezoid. A h ab at v bt v == = = = 2 00 2 0 1 1 44 2 4 = = 19 4 4 2 91 2 0 h A 3. Each rectangle has base 1. The height of each rectangle is Found by using the points t = (.,., ., .) 0515 25 35 in the equation vt t . 2 1 + The area under the curve is approximately 1 5 4 13 4 29 4 53 4 25 +++ = , so the particle is close to x = 25. 4. Each rectangle has base 1. The height of each rectangle is found by using the points y = (.,.,.,.,.) 0515 25 35 45 in the equation t . 2 1 The area under the curve is approximately 1 5 4 13 4 29 4 53 4 85 4 46 25 ++++ = ., so the particle is close to x = 46 25 ..
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Section 5.1 235 5. (a) y 2 x 2 R (b) y x 2 2 Δ x = + 1 2 0 1 2 2 1 2 1 2 2 LRAM: [2(0) ( ) ] +− 2 2 1 2 21 1 1 2 [() ()] + == 2 3 2 3 2 1 2 5 4 1 2 .25 6. (a) y x 2 2 RRAM: 2 1 2 1 2 1 2 2 2 + [ () ()] 11 1 2 2 3 2 3 2 2 2 + 1 2 22 2 1 2 5 4 125 2 . (b) y x 2 2 MRAM: 2 1 4 1 4 1 2 2 3 2 + 4 3 4 1 2 2 5 4 2 + + 5 4 1 2 2 7 4 7 4 2 2 1 2 11 8 1 375 .
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This note was uploaded on 09/26/2010 for the course MATH 135 taught by Professor Noone during the Summer '08 term at Rutgers.

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FDWKCalcSM_ch5 - 234 Section 5.1 Chapter 5 The Definite...

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