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

$$\underset{x\to 0}{\lim }\frac{\cos \mathrm{x}-1+\frac{{\mathrm{x}}^2}{2}-\frac{{\mathrm{x}}^4}{24}}{{\mathrm{x}}^6}$$

Answered by EDWIN88 last updated on 23/Feb/21

$$\underset{x\to 0}{\lim }\frac{1-\frac{{\mathrm{x}}^2}{2}+\frac{{\mathrm{x}}^4}{24}-\frac{{\mathrm{x}}^6}{720}+\mathrm{R}\left({\mathrm{x}}^6\right)-1+\frac{{\mathrm{x}}^2}{2}-\frac{{\mathrm{x}}^4}{24}}{{\mathrm{x}}^6}$$$$=\underset{x\to 0}{\lim }\frac{-\frac{{\mathrm{x}}^6}{720}+\mathrm{R}\left({\mathrm{x}}^6\right)}{{\mathrm{x}}^6}=-\frac{1}{720}$$

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