10.1) Calcule, se existir, cada um dos seguintes limites:

(a) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{\rm sen } (3x)}}{x}$;	(b) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{4x}{{\rm sen }(6x)}$;	(c) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{\rm tg } (3x)}}{x}$;
(d) $\displaystyle\mathop {\lim }\limits_{x \to \pi } \frac{{{\rm sen } x}}{{\pi  - x}}$;	(e) $\displaystyle\mathop {\lim }\limits_{x \to  + \infty } \left(\frac{x}{2}{\rm sen } \frac{\pi }{x}\right)$;	(f) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{\rm sen } x}}{{{e^x} - 1}}$;
(g) $\displaystyle\mathop {\lim }\limits_{x \to {{\frac{\pi }{3}}^ + }} \frac{{{{\cos }^2}(2x)}}{{\cos x - \frac{1}{2}}}$ ;	(h) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{\rm sen } (3x)}}{{{e^{5x}} - 1}}$;	(i) $\displaystyle\mathop {\lim }\limits_{x \to {\pi ^ + }} \frac{3}{{{\rm sen } x}}$.

10.2) Determine o valor real de $k$ de modo que a função definida por \[f\left( x \right) = \left\{ \begin{array}{ll}e^{2x}+k &{\rm{ se }} \;x \leq 0 \\\displaystyle\frac{{\rm sen }(2x)}{x} &{\rm{se }}\; x >0 \\\end{array} \right.\] seja contínua em $x=0$.

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