注 underdot(类)似地，求极限lim_(xto0)(ln(1+x)ln(1-x)-ln(1-x^2))/(x^4).

利用泰勒展开式： \[ \ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + O(x^5), \] \[ \ln(1-x) = -x - \frac{x^2}{2} - \frac{x^3}{3} - \frac{x^4}{4} + O(x^5), \] \[ \ln(1-x^2) = -x^2 - \frac{x^4}{2} + O(x^6). \] 计算得： \[ \ln(1+x)\ln(1-x) = -x^2 + \frac{x^4}{12} + O(x^5), \] \[ \ln(1+x)\ln(1-x) - \ln(1-x^2) = \frac{x^4}{12} + O(x^5). \] 取极限： \[ \lim_{x \to 0} \frac{\frac{x^4}{12} + O(x^5)}{x^4} = \frac{1}{12}. \] 答案：$\boxed{\frac{1}{12}}$