将下列函数展开为幂级数：[tex=8.786x2.786]wO+xnQANIHuRU92XfflXdvAinW/slZkGE/o4SUy4nxS+Eg3T2s3hSRfjTL7DcWaN[/tex]，[tex=2.143x1.214]tdCvNhxRsqsLUuT26x641A==[/tex].

2022-06-01

将下列函数展开为幂级数：[tex=8.786x2.786]wO+xnQANIHuRU92XfflXdvAinW/slZkGE/o4SUy4nxS+Eg3T2s3hSRfjTL7DcWaN[/tex]，[tex=2.143x1.214]tdCvNhxRsqsLUuT26x641A==[/tex].

答案：

因为[tex=1.786x1.357]5GXDBi3fRz6I6Au55YSUHw==[/tex]在全平面解析，所以[tex=3.357x1.143]cXl2AAT3Ma7AQl9LST5yuQ==[/tex].又[tex=22.286x16.5]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[/tex].于是，[tex=1.786x1.357]5GXDBi3fRz6I6Au55YSUHw==[/tex]关于[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]的幂级数展开式为[tex=13.071x2.786]AUSxdYcDOrEX3aQrjVSe9YI100860C0eKgbztpxSVMEA3hDirEcDG9VIJXgCn6L7CmjAlIxc37/cKvvp/F0T9F1TBsSZP/Yk67RC4ecHn9Q=[/tex]，[tex=3.357x1.143]cXl2AAT3Ma7AQl9LST5yuQ==[/tex].

举一反三

内容

0
求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex]（抛物线）隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?
1
在指定的点[tex=0.929x1.0]4C6UdRcYHUV/NV2s+pqOmPoGm9Hqvs15WbPH8LJsPL0=[/tex]的邻域上将下列函数展开为泰勒级数：[tex=1.357x1.357]LsvguIJwOTBmbjrfhkdbcg==[/tex]在[tex=2.143x1.214]ATB4kvGtSubBbAPWkP6VUg==[/tex]
2
将函数[tex=8.786x2.786]/LqTmimv1DBetnXYf1ppel9odHIAFEgXxE8DdjNN9uVDVWMmfvTPzGWtg2BdegxL[/tex] 展开成[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex]的真级数至含 [tex=1.0x1.214]yFat4COBgo7WTPaNshNYVeaf+oyrT5Pl5CmZzxzdlkI=[/tex]的项.
3
将函数[tex=8.786x2.786]/LqTmimv1DBetnXYf1ppel9odHIAFEgXxE8DdjNN9uVDVWMmfvTPzGWtg2BdegxL[/tex] 展开成[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex] 的m级数至含 [tex=0.929x1.214]nl3S1EsI5SJD93W5mL66nQ==[/tex]的项.
4
若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?