高等数学，分段函数在某一点的n阶导数问题
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用泰勒展开：
y = sinx/x = 1-x^2/3!+x^4/5!-x^6/7!+......+(-1)nx^(2n)/(2n+1)!+......
y'(0) = lim<x→0> (-2x/3!+4x^3/5!-6x^5/7+.....) = 0
y''(0) = lim<x→0> (-2/3!+12x^2/5!-30x^4/7+.....) = -1/3
y'''(0) = lim<x→0> (24x/5!-120x^3/7+.....) =0
y^(4)(0) = lim<x→0> (24/5!-720x^2/7+.....) = 1/5
.......................
y^<n>(0) = 0 (n=2k-1, k=1, 2, ......)
y^<n>(0) = (-1)^(n/2)[1/(n+1)] (n=2k, k=1, 2, ......)
y = sinx/x = 1-x^2/3!+x^4/5!-x^6/7!+......+(-1)nx^(2n)/(2n+1)!+......
y'(0) = lim<x→0> (-2x/3!+4x^3/5!-6x^5/7+.....) = 0
y''(0) = lim<x→0> (-2/3!+12x^2/5!-30x^4/7+.....) = -1/3
y'''(0) = lim<x→0> (24x/5!-120x^3/7+.....) =0
y^(4)(0) = lim<x→0> (24/5!-720x^2/7+.....) = 1/5
.......................
y^<n>(0) = 0 (n=2k-1, k=1, 2, ......)
y^<n>(0) = (-1)^(n/2)[1/(n+1)] (n=2k, k=1, 2, ......)
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