Pre-Calc Homework Solutions 228

Pre-Calc Homework Solutions 228 - 1 4(2 1 0 5 26.5 The body...

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3. MRAM 4 : } 1 2 } 1 } 6 6 3 4 } 1 } 1 6 6 4 5 } 1 } 1 6 9 4 5 } 1 } 1 6 0 4 5 } 2 5 4.125 4. RRAM 4 : } 1 2 } 1 } 1 8 5 } 1 3 1 } 2 8 1 } 1 0 2 5 } 1 4 5 } 5 3.75 5. T 4 5 } 1 2 } (LRAM 4 1 RRAM 4 ) 5 } 1 2 } 1 } 1 4 5 } 1 } 1 4 5 } 2 5 3.75 6. E 2 0 (4 x 2 x 3 ) dx 5 3 2 x 2 2 } 1 4 } x 4 4 5 8 2 4 5 4 7. 8. E 5 1 } 1 x } dx 5 3 ln ) x ) 4 5 ln 5 2 ln 1 5 ln 5 < 1.60944 9. (a) E 2 5 f ( x ) dx 52 E 5 2 f ( x ) dx 52 3 The statement is true. (b) E 5 2 2 [ f ( x ) 1 g ( x )] dx 5 E 5 2 2 f ( x ) dx 1 E 5 2 2 g ( x ) dx 5 E 2 2 2 f ( x ) dx 1 E 5 2 f ( x ) dx 1 E 5 2 2 g ( x ) dx 5 4 1 3 1 2 5 9 The statement is true. (c) If f ( x ) # g ( x ) on [ 2 2, 5], then E 5 2 2 f ( x ) dx # E 5 2 2 g ( x ) dx , but this is not true since E 5 2 2 f ( x ) dx 5 E 2 2 2 f ( x ) 1 E 5 2 f ( x ) 5 4 1 3 5 7 and E 5 2 2 g ( x ) dx 5 2. The statement is false. 10. (a) Volume of one cylinder: p r 2 h 5 p sin 2 ( m i ) D x Total volume: V 5 lim n n i 5 1 p sin 2 ( m i ) D x (b) Use p sin 2 x on [0, p ]. NINT( p sin 2 x , x ,0 , p ) < 4.9348 11. (a) Approximations may vary. Using Simpson’s Rule, the area under the curve is approximately } 1 3 } [0 1 4(0.5) 1 2(1) 1 4(2) 1 2(3.5) 1 4(4.5) 1 2(4.75) 1 4(4.5) 1
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Unformatted text preview: 1 4(2) 1 0] 5 26.5 The body traveled about 26.5 m. (b) The curve is always increasing because the velocity is always positive, and the graph is steepest when the velocity is highest, at t 5 6. s 30 t 10 Time (sec) Position (m) 5 1 2 y 4 2 x 2 1 y 4 2 x 2 1 y 4 2 x 2 1 228 Chapter 5 Review n LRAM n MRAM n RRAM n 10 1.78204 1.60321 1.46204 20 1.69262 1.60785 1.53262 30 1.66419 1.60873 1.55752 50 1.64195 1.60918 1.57795 100 1.62557 1.60937 1.59357 1000 1.61104 1.60944 1.60784...
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