级数<img src='https://img2.soutiyun.com/latex/latex.action' />与∑<img src='https://img2.soutiyun.com/latex/latex.action' />满足u_n≤v_n(n=1，2，…)，则( )．

幂级数在区间（2,3）上收敛。（）<img src="http://p.ananas.chaoxing.com/star3/origin/db9bd75eb63772d017847c0c93df5b9c.png"/>

幂级数当x=1/2时的和函数为1/4。（）<img src="http://p.ananas.chaoxing.com/star3/origin/043254ab016912303dd0ee1f12e9e6cf.png"/>

幂级数当x=-1/2时的和函数为（）。 <img src='\"http://p.ananas.chaoxing.com/star3/origin/9984d379d3b62cbd8a517c30c8076973.png\"/'/>

是f(x)展开成三角级数。（） <img src='\"http://p.ananas.chaoxing.com/star3/origin/2516f5143defae199c0288cc5e2782ff.png\"/'/>

设a为常数，则级数<img src='https://img2.soutiyun.com/latex/latex.action' />( )．

已知两个线性变换<img src='https://img2.soutiyun.com/ask/2020-07-24/964447450539867.png' />，求从<img src='https://img2.soutiyun.com/ask/2020-07-24/964447482729708.png' />到<img src='https://img2.soutiyun.com/ask/2020-07-24/964447490132131.png' />的线性变换。

幂级数<img src='https://img2.soutiyun.com/latex/latex.action' />的收敛域为( )．

设a为常数，则级数<img src='https://img2.soutiyun.com/ask/uploadfile/6681001-6684000/7528d38b5c08d705855c25ce86a7ee6d.png' />( )

若级数<img src='https://img2.soutiyun.com/latex/latex.action' />与<img src='https://img2.soutiyun.com/latex/latex.action' />分别收敛于S₁与S₂，则( )式未必成立．

设f(x)以2π为周期，<img src='https://img2.soutiyun.com/ask/uploadfile/6681001-6684000/04820dd60870b1dd31e972d33b85c0e5.png' />，s(x)为f(x)的傅里叶级数、和函数，则( )

已知z=lnu，<img src='https://img2.soutiyun.com/latex/latex.action' />，则<img src='https://img2.soutiyun.com/latex/latex.action' />( )

级数<img src='https://img2.soutiyun.com/latex/latex.action' />收敛，则必有( )．

设<img src='https://img2.soutiyun.com/latex/latex.action' />则<img src='https://img2.soutiyun.com/latex/latex.action' />=( )．

幂级数<img src='https://img2.soutiyun.com/latex/latex.action' />的收敛半径R=( )．

当( )时，无穷级数<img src='https://img2.soutiyun.com/latex/latex.action' />(u＞0)绝对收敛．

利用幂级数展开，计算<img src='https://img2.soutiyun.com/shangxueba/ask/51432001-51435000/51432829/980695520313543.png' />。

幂级数<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671982/2015102915280779420.jpg' />

病历摘要：脑膜瘤患者女，55岁，视力下降数月。查体：视力下降，余神经体征阴性。<img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411361155670.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411363213140.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411363770796.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411364194722.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411364682394.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/21054001-21057000/21056152/2016080411365145350.jpg' />

将函数f(x)＝x²在<img src='https://img2.soutiyun.com/shangxueba/ask/18735001-18738000/18737342/2016071617062459326.jpg' />上展开成余弦级数，其形式为<img src='https://img2.soutiyun.com/shangxueba/ask/18735001-18738000/18737342/2016071617063532608.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/18735001-18738000/18737342/2016071617065141640.jpg' />（）<img src='https://img2.soutiyun.com/shangxueba/ask/18735001-18738000/18737342/2016071617071375522.jpg' />

设<img src='https://img2.soutiyun.com/shangxueba/ask/51291001-51294000/51293683/975264374908477.png' />是n维实向量,且<img src='https://img2.soutiyun.com/shangxueba/ask/51291001-51294000/51293683/975264387229182.png' />战性无关,<img src='https://img2.soutiyun.com/shangxueba/ask/51291001-51294000/51293683/975264401121976.png' /><img src='https://img2.soutiyun.com/shangxueba/ask/51291001-51294000/51293683/975264415373792.png' />是线性方程组

级数<img src='http://221.174.24.96:6088/latex/latex.action？latex=xhn1bv97bj0xfv57k1xpbmz0ex0oltepxntufvxmcmfjezj9e259' />是否收敛？若收敛，是条件收敛还是绝对收敛？

（2013）正项级数<img src='https://img2.soutiyun.com/shangxueba/ask/19032001-19035000/19033100/2015110315490562976.png' />的部分和数列<img src='https://img2.soutiyun.com/shangxueba/ask/19032001-19035000/19033100/2015110315495812105.png' />有上界是该级数收敛的：（）

若<img src='https://img2.soutiyun.com/latex/latex.action' />，<img src='https://img2.soutiyun.com/latex/latex.action' />试证明时域卷积定理<img src='https://img2.soutiyun.com/latex/latex.action' />和频域卷积定理<img src='https://img2.soutiyun.com/latex/latex.action' />

男，4个月，相貌怪异，结合图像，最可能的诊断（）<img src='https://img2.soutiyun.com/shangxueba/ask/17796001-17799000/17798971/201511231032013640.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/17796001-17799000/17798971/2015112310320224881.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/17796001-17799000/17798971/201511231032042853.jpg' /><img src='https://img2.soutiyun.com/shangxueba/ask/17796001-17799000/17798971/2015112310320644602.jpg' />