题目

设f(x)是定义在R上的奇函数，且对任意实数x，恒有f(x＋2)＝－f(x)．当x∈[0,2]时，f(x)＝2x－x2. (1)求证：f(x)是周期函数； (2)当x∈[2,4]时，求f(x)的解析式； (3)计算f(0)＋f(1)＋f(2)＋…＋f(2 012)． 答案：解：(1)∵f(x＋2)＝－f(x)， ∴f(x＋4)＝－f(x＋2)＝f(x)． ∴f(x)是周期为4的周期函数． (2)当x∈[－2,0]时，－x∈[0,2]，由已知得 f(－x)＝2(－x)－(－x)2＝－2x－x2， 又f(x)是奇函数，∴f(－x)＝－f(x)＝－2x－x2， ∴f(x)＝x2＋2x. 又当x∈[2,4]时，x－4∈[－2,0]， ∴f(x－4)＝(x－4)2＋2(x－4)． 又f(x)是周期为4的周期函数， Every one of us ,rich or poor, should at least have one or two good friends. Your friends will you when you speak, will take care of you when you are sick, and will be together you in your journey through life.Everyone friends. Friendship can make us happier. can we find a good friend and get on well with each other? Here some advice. friends with a person who is easy to get along with.You should make friends with a person who has in common with you.。Give your friend a when he or she is in trouble .Friends should always be ready to each other.Believe(相信) in each other. This is the most thing in a friendship.Even the best friends may have . sometimes. this happens, don’t let it last too long. Try to make up with(和好) your soon. is a kind of treasure(珠宝) in our life . It a bottle of wine(白酒), the longer it is kept, the better it will be.1.A. listen to B. hear C. sound D. listen2.A. for B. from C. with D. at3.A. get B. want C. have D. needs4.A. What B. When C. How D. Where5.A. has B. have C. are D. is6.A. Making B. Makes C. Made D. Make7.A. nothing B. everything C. something D. anything8.A. book B. hand C. pen D. map9.A. help B. helping C. to help D. helps10.A. loudly B. outgoing C. important D. quietly11.A. a fight B. a laugh C. a point D. a result12.A. Before B. If C. While D. As13.A. parents B. teachers C. classmates D. friends14.A. Book B. Friend C. Friendship D. Teacher15.A. is like B. look like C. is liking D. feel like