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Evaluate : \( \lim _{x \rightarrow 0} \frac{1-\cos 3 x}{x^{2}} \) |
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Answer» \(\lim\limits_{x\to0}\frac{1-cos3x}{x^2}\) \(=\lim\limits_{x \to 0}\cfrac{1-(1-\frac{(3x)^2}{2!}+\frac{(3x)^4}{4!}-....)}{x^2}\) \(=\lim\limits_{x \to 0}\cfrac{\frac{9x^2}2-\frac{81x^4}{24}+...}{x^2}\) \(=\lim\limits_{x \to 0}\frac92-\frac{81}{24}x^2+....\) \(=\frac92\) (By taking limit) |
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