Đáp án: C
Giải thích các bước giải:
$\begin{array}{l}
\mathop {\lim }\limits_{x \to 0} \left( {x\sin \frac{2}{x}} \right)\\
= \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{2.\frac{2}{x}}}.\sin \frac{2}{x}} \right)\\
= \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{2}.\frac{{\sin \frac{2}{x}}}{{\frac{2}{x}}}} \right)\\
= \frac{1}{2}\left( {do:\mathop {\lim }\limits_{x \to 0} \frac{{\sin u}}{u} = 1\,} \right)\\
\Rightarrow hs\,liên\,tục: \Rightarrow a.cos0 - 5 = \frac{1}{2}\\
\Rightarrow a - 5 = \frac{1}{2}\\
\Rightarrow a = \frac{{11}}{2}
\end{array}$
