7. (10 points) Recall that the hyperbolic tangent function
tanh x=,x∈R
is one to one and has the inverse function f(x) = tanh-1x. Find the Maclaurin series off(x) = tanh-1x.

詳解 (共 1 筆)

助人為本
助人為本
詳解 #7409300
2026/06/16
所以要解這題
看到tanh-1x
要想到其微分等於
6a30ac81a90c5.jpg
級數要想到等比級數的延伸
所以可以寫成1+x^2+x^4+...
所以再積分回去變成
6a30acca4cf8c.jpg