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Course: Calculus
\(\underset{x\to 1 }{\mathop{\lim }}\,\frac{1-x+\ln x}{1+\cos (\pi x)}\) = ?
   \(\frac{\pi }{2}\)
   \(\pi \)
   \(\frac{1}{\pi }\)
   \(-\frac{1}{{{\pi }^{2}}}\)
   \(\ln 1\)