for those who have calculus by apostol vol.1, i refer to page 288. i am looking at the first example where he proves that tanx = x + (1/3)x(adsbygoogle = window.adsbygoogle || []).push({}); ^{3}+ o(x^{3}). he showed that 1/cosx = 1 + (1/2)x^{2}+ o(x^{2}) and therefore tanx = sinx / cosx = (x - (1/6)x^{3}+ o(x^{4}))(1 + (1/2)x^{2}+ o(x^{2})) and that should equal x + (1/3)x^{3}+ o(x^{3}).

i multiplied it out and got x + (1/3)x^{3}+ o(x^{3}) - (1/12)x^{5}- o(x^{5}) +o(x^{4}) + o(x^{6}) + o(x^{4})o(x^{2}).

my question is where did the rest of the o's go and how come you are only left with o(x^{3})? why not o(x^{4})?

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# Homework Help: Little o notation trouble

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