搜搜考试网一道AP微积分题Which of the following functions is not odd?有个选项我知道它
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一道AP微积分题
Which of the following functions is not odd?
有个选项我知道它是odd function,但只有感觉,无法从式子上看出来：
f(x)=x/(x^2+1),怎么把它化成多项式的样子再直接通过次数判断奇偶?
Which of the following functions is not odd?
有个选项我知道它是odd function,但只有感觉,无法从式子上看出来：
f(x)=x/(x^2+1),怎么把它化成多项式的样子再直接通过次数判断奇偶?
这个好办,不就是想把f(x)=x/(x^2+1),展开成幂级数吗.
积分f（x）=1/2ln(1+x~2)+c=1/2(x~2-1/2x~4+.)
后面是taylor展开,不过把x换成x~2而已.
之后再两边求导,发现右边的幂级数所有的x的指数一定是奇数.
因此是奇函数
再问： 不懂什么叫taylor展开= = 没关系你不用在这里详细解释了，在后面的微积分学习中能学到么？
再答： 是的，你问的内容恰恰是在那个部分要学的。
积分f（x）=1/2ln(1+x~2)+c=1/2(x~2-1/2x~4+.)
后面是taylor展开,不过把x换成x~2而已.
之后再两边求导,发现右边的幂级数所有的x的指数一定是奇数.
因此是奇函数
再问： 不懂什么叫taylor展开= = 没关系你不用在这里详细解释了，在后面的微积分学习中能学到么？
再答： 是的，你问的内容恰恰是在那个部分要学的。
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