ln(1-x^2)泰勒展开3层.

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ln(1-x^2)泰勒展开3层.ln(1-x^2)泰勒展开3层.ln(1-x^2)泰勒展开3层.f''(x)=-2x/(1-x²)f''''(x)=[-2(1-x²)-(-2x)(-2x

ln(1-x^2)泰勒展开3层.
ln(1-x^2)泰勒展开3层.

ln(1-x^2)泰勒展开3层.
f'(x)=-2x/(1-x²)
f''(x)=[-2(1-x²)-(-2x)(-2x)]/(1-x²)²=-2(1+x²)/(1-x²)²
f(3) (x)=-2[2x(1-x²)²-2(1-x²)(-2x)(1+x²)]/(1-x²)^4
(tylor's series of aproximation of x=a)=f(a)+f'(a)(x-a)+f''(a)(x-a)²/2!+[f(3)(a)](x-a)³/3!
a值应该是书上给你的,没给就直接写a

书上的公式只有ln(1+x)的
ln(1+x)=x-(1/2)x^2+……+o(x^n)
老师肯定也讲了ln(1-x)的
那么
ln(1-x^2)=ln(1+x)+ln(1-x)
=x-(1/2)x^2+(1/3)x^3+o(x^3)+[-x-(1/2)x^2-(1/3)x^3+o(x^3)]
=-x^2+o(x^3)