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{(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 .
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