Problem 6. Compute the following:
a) $\lim_{x \to 0} x \left( \int_0^x \cos\left(\frac{1}{t+1}\right) dt \right)$, b) $\lim_{x \to 0^+} \frac{\tan x - x}{x^3}$, $x \in \left(0, \frac{\pi}{2}\right)$, c) $\lim_{x \to 0^+} xe^{\left(\frac{1}{x}\right)}$.
