一、题目
以下函数 $f[g(x)]$ 以 $x=0$ 为第二类间断点的是哪个?
(A) $f(u)=\ln \left(1+u^{2}\right), g(x)=\left\{\begin{array}{ll}\sin ^{2} x+(x+1)^{2}, & x \leqslant 0, \\ x^{2}+1, & x>0 .\end{array}\right.$
(B) $f(u)=\left\{\begin{array}{ll}1-u, & u \leqslant 0, \\ u^{2}+1, & u>0,\end{array}, g(x)=2 \cos x-1\right.$.
(C) $f(u)=\left\{\begin{array}{ll}\frac{\ln \left(1-u^{2}\right)}{u} \sin \frac{1}{u}, & u<0, \\ 1-\cos \sqrt{u}, & u \geqslant 0,\end{array}, g(x)=\left\{\begin{array}{ll}x, & x<0, \\ x+\frac{\pi^{2}}{4}, & x \geqslant 0 .\end{array}\right.\right.$.
(D) $f(u)=\mathrm{e}^{u^{2}}+1, g(x)=\left\{\begin{array}{ll}\frac{1}{x}, & x<0, \\ 0, & x=0, \\ \sin \frac{1}{x}, & x>0 .\end{array}\right.$
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