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
詳解 #7409300
所以要解這題
看到tanh-1x
要想到其微分等於

該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
