本题目来源于试卷: Proofs Proofs ，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
$f^{(n)}(x)=\left(\frac{1}{4}\right)^{n} \frac{(2 n)!}{n!}(1-x)^{-1 / 2-n} \quad n \in \mathbb{Z}$, $\quad n \geq 2$
Let $g(x)=\cos (m x), 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:
| 
