Pre-Calc Homework Solutions 47

Pre-Calc Homework Solutions 47 - Section 2.1 (b) The...

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(b) The average speed over the interval from time t 5 3 to time 3 1 h is } D D y t } 55 } 4.9(6 h h 1 h 2 ) } 5 29.4 1 4.9 h Since lim h →0 (29.4 1 4.9 h ) 5 29.4, the instantaneous speed is 29.4 m/sec. 58. (a) y 5 gt 2 20 5 g (4 2 ) g 5 } 2 1 0 6 } 5 } 5 4 } or 1.25 (b) Average speed 5 } 2 4 0 } 5 5 m/sec (c) If the rock had not been stopped, its average speed over the interval from time t 5 4 to time t 5 4 1 h is } D D y t } } 1.25(8 h h 1 h 2 ) } 5 10 1 1.25 h Since lim h →0 (10 1 1.25 h ) 5 10, the instantaneous speed is 10 m/sec. 59. (a) (b) The limit appears to be 0. 60. (a) (b) There is no clear indication of a limit. 61. (a) (b) The limit appears to be approximately 2.3. 62. (a) (b) The limit appears to be 0. 63. (a) Because the right-hand limit at zero depends only on the values of the function for positive x -values near zero. (b) Area of n OAP 5 } 1 2 } (base)(height) 5 } 1 2 } (1)(sin u ) 5 } sin 2 u } Area of sector 5 } (angle)( 2 radius) 2 }5} u ( 2 1) 2 } 5 } u 2 } Area of n OAT 5 } 1 2 } (base)(height) 5 } 1 2 } (1)(tan u ) 5 } tan 2 u } (c) This is how the areas of the three regions compare.
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