1) Tìm các giới hạn sau:
$a) \mathop {\lim }\limits_{x \to 0}\frac{1-\cos 5x \cos 7x}{\sin^2 11x} $
giải
$\mathop {\lim }\limits_{x \to 0}\frac{1-\cos 5x \cos 7x}{\sin^2 11x} = \mathop {\lim }\limits_{x \to 0}\frac{1-cos12x+1-cos2x}{2sin^211x}$
$=\mathop {\lim }\limits_{x \to 0}\frac{sin^26x+sin^2x}{sin^211x}=\mathop {\lim }\limits_{x \to 0}\frac{36.(\frac{sin6x}{6x})^2+(\frac{sinx}{x})^2}{121.(\frac{sin11x}{11x})^2}=\frac{37}{121}.$
* ko biết sai chỗ nào nữa.