Problem 820 (difficulty: 4/10)

\(\displaystyle \lim_{x\to0} \log_{(1-x^2)} (\cos bx) = ? \qquad \lim_{x\to0}\left(\frac{1+e^x}{1+\cos x}\right)^{\ctg x}=? \qquad \lim_{x\to0}\frac{2\cth (x^2)-\ctg(1-\cos x)}{\ln(1+x)-\sin x}=? \)

Give me another random problem!