(b)The average speed over the interval from time t53 totime 31his}DDyt}55}4.9(6hh1h2)}529.414.9hSince limh→0(29.414.9h)529.4, the instantaneousspeed is 29.4 m/sec.58. (a)y5gt2205g(42)g5 }2106} 5 }54}or 1.25(b)Average speed 5 }240} 55 m/sec(c)If the rock had not been stopped, its average speed overthe interval from time t54 to time t541his}DDyt}}1.25(8hh1h2)}51011.25hSince limh→0(1011.25h)510, the instantaneous speedis 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 onthe values of the function for positive x-values nearzero.(b)Area of nOAP5 }12}(base)(height)5 }12}(1)(sin u) 5 }sin2u}Area of sector 5}(angle)(2radius)2}5}u(21)2} 5 }u2}Area of nOAT5 }12}(base)(height) 5 }12}(1)(tan u)5 }tan2u}(c)This is how the areas of the three regions compare.
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