How was the $o(x)$ in this formula calculated？

Asked Nov 18 '21 at 14:37

Active Nov 18 '21 at 14:43

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In this Equivalent Infinitesimal Replacement shown in the figure, there is such a formula $$ e^{\sin^2x}-1+\sqrt{1-\cos x} \sim \sqrt{\frac{1}{2}}x+o(x) \sim \sqrt\frac{1}{2}x $$ What's the meaning of $o(x)$? How did it come about? Why can we ignore it?

edited Nov 18 '21 at 14:43

asked Nov 18 '21 at 14:37

Twilight Lee

1

https://mathworld.wolfram.com/LandauSymbols.html – Xander Henderson Nov 18 '21 at 14:39
Please do not use image for the critical part of the question. – Lee David Chung Lin Nov 19 '21 at 10:03

How was the $o(x)$ in this formula calculated？

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