【求助】泰勒公式部分，tanx的迈克劳林展开式

Question

如题所述

Answer 1

tan0 = 0;
(tanx)' = (secx)^2, (tan0)' = 1;
(tanx)'' = 2tanx(secx)^2, (tan0)'' = 0;
(tanx)''' = 2(secx)^4 + 4(tanx)^2(secx)^2, (tan0)''' = 2;

(tanx)^(4) = 16tanx(secx)^4 + 8(tanx)^3(secx)^2, (tan0)^(4) = 0;
(tanx)^(5) = 16(secx)^6 + 88(tanx)^2(secx)^4 + 16(tanx)^4(secx)^2, (tan0)^(5) = 16;
.............................
tanx = x + 2x^3/3! + 16x^5/5! + ...... = x + x^3/3 + 2x^5/15 + ......

Answer 2

如图

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