Could you help me calculate the following limits:
$\lim_{x \to 0} x \left[ \frac{1}{x} \right]$
$\lim_{x\to 0} \frac{1-\cos x \cdot \sqrt{\cos2x} }{x^2}$
$\lim_{x\to 10} \frac{\log _{10}(x) - 1}{x-10}$
As to the last one I thought I could use $\lim\frac{log _{a}(1+\alpha)}{\alpha} = \log_ae$ but it wouldn't work