Tìm giới hạn \(B=\lim\limits _{x \rightarrow 0} \frac{1-\cos x \cdot \cos 2 x \cdot \cos 3 x}{x^{2}}\)

* Hướng dẫn giải

Ta có 

\(\dfrac{1-\cos x \cdot \cos 2 x \cdot \cos 3 x}{x^{2}}=\dfrac{1-\cos x+\cos x \cos 2 x(1-\cos 3 x)+\cos x(1-\cos 2 x)}{x^{2}}\)

\(\begin{array}{l} =\dfrac{1-\cos x}{x^{2}}+\cos x \cdot \cos 2 x \dfrac{1-\cos 3 x}{x^{2}}+\cos x \dfrac{1-\cos 2 x}{x^{2}} \\ B=\lim\limits _{x \rightarrow 0} \dfrac{1-\cos x}{x^{2}}+\lim \limits_{x \rightarrow 0} \cos x \cdot \cos 2 x \dfrac{1-\cos 3 x}{x^{2}}+\lim\limits _{x \rightarrow 0} \cos x \dfrac{1-\cos 2 x}{x^{2}}=3 \end{array}\)