将cosx在x=π/4处展开成幂级数,求详解.
人气:196 ℃ 时间:2020-03-25 01:57:27
解答
cosx=cos(π/4+x-π/4)
=cosπ/4cos(x-π/4)-sinπ/4sin(x-π/4)
=√2/2 [cos(x-π/4)-sin(x-π/4)]
=√2/2× 【1-(x-π/4)^2/2!+(x-π/4)^4/4!-.-[(x-π/4)-(x-π/4)^3/3!+(x-π/4)^5/5!+.]】
x∈R
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