Pre-Calc Homework Solutions 209

Pre-Calc Homework Solutions 209 - partition of [ 2 p , p ]....

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3. The graph has jump discontinuities at all integer values, but the Riemann sums tend to the area of the shaded region shown. The area is the sum of the areas of 5 rectangles (one of them with height 0): E 5 0 int( x ) dx 5 0 1 1 1 2 1 3 1 4 5 10. [ 2 2.7, 6.7] by [ 2 1.1, 5.1] Quick Review 5.2 1. 5 n 5 1 n 2 5 (1) 2 1 (2) 2 1 (3) 2 1 (4) 2 1 (5) 2 5 55 2. 4 k 5 0 (3 k 2 2) 5 [3(0) 2 2] 1 [3(1) 2 2] 1 [3(2) 2 2] 1 [3(3) 2 2] 1 [3(4) 2 2] 5 20 3. 4 j 5 0 100( j 1 1) 2 5 100[(1) 2 1 (2) 2 1 (3) 2 1 (4) 2 1 (5) 2 ] 5 5500 4. 99 k 5 1 k 5. 25 k 5 0 2 k 6. 500 k 5 1 3 k 2 7. 2 50 x 5 1 x 2 1 3 50 x 5 1 x 5 50 x 5 1 (2 x 2 1 3 x ) 8. 8 k 5 0 x k 1 20 k 5 9 x k 5 20 k 5 0 x k 9. n k 5 0 ( 2 1) k 5 0 if n is odd. 10. n k 5 0 ( 2 1) k 5 1 if n is even. Section 5.2 Exercises 1. lim )) P )) 0 n k 5 1 c k 2 D x k 5 E 2 0 x 2 dx where P is any partition of [0, 2]. 2. lim )) P )) 0 n k 5 1 ( c k 2 2 3 c k ) D x k 5 E 5 2 7 ( x 2 2 3 x ) dx where P is any partition of [ 2 7, 5]. 3. lim )) P )) 0 n k 5 1 } c 1 k }D x k 5 E 4 1 } 1 x } dx where P is any partition of [1, 4]. 4. lim )) P )) 0 n k 5 1 } 1 2 1 c k }D x k 5 E 3 2 } 1 2 1 x } dx where P is any partition of [2, 3]. 5. lim )) P )) 0 n k 5 1 ˇ 4 w 2 w c w k 2 w D x k 5 E 1 0 ˇ 4 w 2 w x w 2 w dx where P is any par- tition of [0, 1]. 6. lim )) P )) 0 n k 5 1 (sin 3 c k ) D x k 5 E p 2 p sin 3 x dx where P is any
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Unformatted text preview: partition of [ 2 p , p ]. 7. E 1 2 2 5 dx 5 5[1 2 ( 2 2)] 5 15 8. E 7 3 ( 2 20) dx 5 ( 2 20)(7 2 3) 5 2 80 9. E 3 ( 2 160) dt 5 ( 2 160)(3 2 0) 5 2 480 10. E 2 1 2 4 } p 2 } d u 5 } p 2 } [ 2 1 2 ( 2 4)] 5 } 3 2 p } 11. E 3.4 2 2.1 0.5 ds 5 0.5[3.4 2 ( 2 2.1)] 5 2.75 12. E ˇ 1 w 8 w ˇ 2 w ˇ 2 w dr 5 ˇ 2 w ( ˇ 1 w 8 w 2 ˇ 2 w ) 5 4 13. Graph the region under y 5 } 2 x } 1 3 for 2 2 # x # 4. E 4 2 2 1 } 2 x } 1 3 2 dx 5 } 1 2 } (6)(2 1 5) 5 21 14. Graph the region under y 5 2 2 x 1 4 for } 1 2 } # x # } 3 2 } . E 3/2 1/2 ( 2 2 x 1 4) dx 5 } 1 2 } (1)(3 1 1) 5 2 y 5 4 3 2 1 x 5 x = 3 2 x = 1 2 y 5 x 5 Section 5.2 209...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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