设f0（x）=sinx，f1（x）=f0′（x），f2（x）=f1′（x），…，fn+1（x）=fn′（x），n∈N，则f2010（x）=（ ）
A．cosx
B．-cosx
C．sinx
D．-sinx
由题意f0（x）=sinx，f1（x）=f0′（x）=cosx，f2（x）=f1′（x）=-sinx，f3（x）=f2′（x）=-cosx，f4（x）=f3′（x）=sinx，由此可知，在逐次求导的过程中，所得的函数呈周期性变化，从0开始计，周期是4，∵2011=4×502+3，f2010（x）是一周中的第三个函数，故f2010（x）=-sinx
故选D
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| Carolyn Stradley is the founder of C&S Paving Inc(铺路公司)in Atlanta, USA. In the following account. She recalls the job that challenged her 1 and skill but left her flying high. ¨When the Atlanta Airport was under 2 . in 1979, we were a new company struggling to make it National Car Rental wanted to have 2,500 square meters of dirt paved 3 the cars could be on site 4 the airport opened. and the official opening was only ten days away ! 5 other local paving company wanted to do the job, 6 it couldn't be done. in such a short time. " " Because we were new and really needed the work ,we were 7 to try harder. We gave National Car Rental our offer and 8 our best effort to get the job finished within ten days. We also 9 them that if we failed,they would be no worse off, 10 they had plenty to gain if we succeeded. " "We got the job and immediately went into 11 . Working at night needed lights, so I rented a machine to produce electricity for the site. Our 12 challenge was to keep the rock mixture 13 enough. All the available water wagons (洒水车) were rented out for the airport construction,and we certainly couldn't afford to buy a new one. 14 ,I got a special 15 To rent fire engine hoses (消防水龙带) and connect them to nearby hydrants (消 防栓);then I 16 held one of those hoses to 17 down the rock. ' "Those ten days were filled with challenges that 18 one creative idea after another. Nine days later, the night before the airport opened , National Car Rental was the 19 company that had cars on the parking lot. " "The key to our success was having the 20 to take on any job and then being creative in our approach to getting it done. " | ||||
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