将cosx在x=π/4处展开成幂级数,求详解.
题目
将cosx在x=π/4处展开成幂级数,求详解.
答案
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
举一反三
已知函数f(x)=x,g(x)=alnx,a∈R.若曲线y=f(x)与曲线y=g(x)相交,且在交点处有相同的切线,求a的值和该切线方程.
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
最新试题
热门考点