问题 填空题

若f0(x)=sinx,f1(x)=f0′(x),f2(x)=f1′(x),…,fn+1(x)=fn′(x),n∈N,则f2009′(x)=______.

答案

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,

∵2009=4×502+1,f2009(x)是一周中的第一个函数,故f2009(x)=cosx

故答案为cosx

完形填空
The happy Prince was blind﹙瞎﹚。The swallow﹙燕子﹚sat on his shoulder and told him many   __.
He told him about so many amazing places __  __ Nile River﹙尼罗河﹚,the desert in Africa and so on. The Happy Prince greatly enjoyed his stories. He wanted to know   __ was happening in the city, so he asked the swallow to fly over the city to have a look. The Swallow did as the Prince asked. He _  ___ through the sky. Below him, he saw rich people living __ __ in their homes. He saw poor people were in cold and hunger.__  __ one bridge, two boys shook their bodies t stay warm. The Swallow told the Prince everything. The Happy Prince became even __  _ and told the Swallow to take his gold to the cold and hungry people. Heavy snow fell off the sky on the city. Life for the swallow was becoming more difficult._  __ he still didn’t leave the Prince, he flew to the Prince’s shoulder fell dead at his feet. At the same time, there was a loud“Crack”and the Prince _  _  two halves, he might be very sad.The next morning, people in the city found them_  _ and took them out of the square. The angel found them and made them live forever in the city of gold.
小题1:
A.magazinesB.storiesC.novelsD.words
小题2:
A.such asB.at leastC.so farD.because of
小题3:
A.howB.whatC.whyD.when
小题4:
A.walkedB.ranC.flewD.rode
小题5:
A.normallyB.surprisinglyC.comfortablyD.personally
小题6:
A.FromB.InC.UnderD.With
小题7:
A.sadderB.happierC.sadD.happy
小题8:
A.AndB.ButC.SoD.Because
小题9:
A.brought outB.fell downC.made upD.broke into
小题10:
A.bothB.allC.eachD.none
选择题