a) Giải phương trình: 2cosx - căn 2  = 0

a)\(2\cos x - \sqrt 2 = 0\)

\( \Leftrightarrow cosx = \frac{{\sqrt 2 }}{2}\)

\( \Leftrightarrow cosx = cos\frac{\pi }{4}\)

\[ \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{4} + k2\pi \end{array} \right.\]

b)\[f(x) = \frac{{5x - 15}}{{\left( {9 - {x^2}} \right)\left( {\sqrt {5x - 6} + 3} \right)}}\,.\]

\[f(x) = \frac{{5(x - 3)}}{{\left( {3 - x} \right)\left( {3 + x} \right)\left( {\sqrt {5x - 6} + 3} \right)}}\,.\]

\[f(x) = \frac{{ - 5}}{{\left( {3 + x} \right)\left( {\sqrt {5x - 6} + 3} \right)}}\,.\]

\(\mathop {\lim }\limits_{x \to 3} {\mkern 1mu} \,f(x) = \frac{{ - 5}}{{36}}\)