Question

设f0(x)＝cos x，f1(x)＝f0′(x)，f2(x)＝f1′(x)，…，fn＋1(x)＝fn′(x)，n∈

N，则f2 011(x)等于 ( )．

A．sin x B．－sin x

C．cos x D．－cos x

 

Answer 1

A

【解析】f0(x)＝cos x，f1(x)＝－sin x，f2(x)＝－cos x，

f3(x)＝sin x，f4(x)＝cos x，…，

由此看出，四个一循环，具有周期性，T＝4.∵2 011＝4×502＋3，∴f2 011(x)＝f3(x)＝sin x.