lim-x-0-cos-x-1-x-2-2-x-4-24-x-6-

Question Number 133583 by bemath last updated on 23/Feb/21

\lim_{x \to 0} \frac{\cos x - 1 + \frac{x^{2}}{2} - \frac{x^{4}}{24}}{x^{6}}

Answered by EDWIN88 last updated on 23/Feb/21

\lim_{x \to 0} \frac{1 - \frac{x^{2}}{2} + \frac{x^{4}}{24} - \frac{x^{6}}{720} + R (x^{6}) - 1 + \frac{x^{2}}{2} - \frac{x^{4}}{24}}{x^{6}}

= \lim_{x \to 0} \frac{- \frac{x^{6}}{720} + R (x^{6})}{x^{6}} = - \frac{1}{720}

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