(2)lim_(xto0)[(1)/(ln(1+tan^2)x)-(1)/(ln(1+x^2))]

利用泰勒展开式近似： \[ \ln(1+\tan^2 x) \approx x^2 + \frac{x^4}{6}, \quad \ln(1+x^2) \approx x^2 - \frac{x^4}{2}. \] 则 \[ \frac{1}{\ln(1+\tan^2 x)} \approx \frac{1}{x^2} - \frac{1}{6}, \quad \frac{1}{\ln(1+x^2)} \approx \frac{1}{x^2} + \frac{1}{2}. \] 相减得 \[ \lim_{x\to0}\left[\frac{1}{\ln(1+\tan^2 x)} - \frac{1}{\ln(1+x^2)}\right] = -\frac{1}{6} - \frac{1}{2} = -\frac{2}{3}. \] 答案：$\boxed{-\frac{2}{3}}$