Maclaurin Series (id: b64736e39)

本题目来源于试卷: Maclaurin Series，类别为 IB数学

[问答题]
Let $f(x)=\frac{1}{\sqrt{1-x}}$, x<1 .
1. Show that $f^{\prime \prime }(x)=\frac{3}{4}(1-x{)}^{-5/2}$.
2. Use mathematical induction to prove that

$f^{(n)}(x)={\left(\frac{1}{4}\right)}^n\frac{(2n)!}{n!}(1-x{)}^{-1/2-n}n\in \mathbb{Z},n\ge 2$.


Let $g(x)=\cos (mx),m\in \mathbb{Q}$ .
Consider the function h defined by $h(x)=f(x)\times g(x)$ for x<1 .
The x^{2} term in the Maclaurin series for h(x) has a coefficient of $-\frac{3}{4}$ .
3. Find the possible values of m .

参考答案:

本题详细解析: 暂无

微信扫一扫，分享更方便