设f（x)是以T为周期的连续周期函数（-∞＜x＜+∞).证明:

A . -4 B . 4 C . -16 D . 16

A . -3 B . 3 C . -9 D . 9

A .https://assets.asklib.com/psource/201510291530231830.jpg B .https://assets.asklib.com/psource/2015102915303768116.jpg C .https://assets.asklib.com/psource/2015102915305046680.jpg D .https://assets.asklib.com/psource/2015102915310234816.jpg

A . ['y=f（x）+chttps://assets.asklib.com/psource/2015102616471385225.jpg B . y=f（x）https://assets.asklib.com/psource/2015102616471475863.jpg -https://assets.asklib.com/psource/2015102616471475863.jpg +cC . y=f（x）-1+chttps://assets.asklib.com/psource/2015102616471385225.jpg D . y=f（x）-1+chttps://assets.asklib.com/psource/2015102616471475863.jpg

A .https://assets.asklib.com/psource/2015102816494294239.jpg B .https://assets.asklib.com/psource/2015102816495840213.jpg C .https://assets.asklib.com/psource/2015102816501252670.jpg D .https://assets.asklib.com/psource/2015102816502734467.jpg

1 ) ( £ x f ) ( ) ( x f x X P = = 0 ) ( ³ x f ) ( ) ( x F x f = ¢

A.T B.2T C.12T D.T/12

设f(x，y)为连续函数，<img src='https://img2.soutiyun.com/ask/uploadfile/2766001-2769000/13ad2684e5aab0b425f536ce4ab309b3.jpg' />（）<img src='https://img2.soutiyun.com/ask/uploadfile/2766001-2769000/1cb1d88a2e4e034baf23759c42df09f5.jpg' /><img src='https://img2.soutiyun.com/ask/uploadfile/2766001-2769000/99fe3f313cd296681f496a61f8bd3f0d.jpg' /><img src='https://img2.soutiyun.com/ask/uploadfile/2766001-2769000/5e9f42f3b66e17f1010eb8405d5e6d3b.jpg' /><img src='https://img2.soutiyun.com/ask/uploadfile/2766001-2769000/5fbc012b3e13b4f4e8fbc129a807492f.jpg' />

A．f(1)； B．f(0)； C．1； D．f(0)-f(1)．

A．P(X＞b)=1-F(b) B．P(X=a)=0 C．<img src='https://img2.soutiyun.com/ask/uploadfile/6663001-6666000/4542cc99e5c66e758cc6e88d9f65e164.png' />D．<img src='https://img2.soutiyun.com/ask/uploadfile/6663001-6666000/60caca0148aa7397cd929e9d3025f1d9.png' />

设f(x)为[-a，a]上的连续函数，证明： (1)若f(x)是偶函数，则<img src='https://img2.soutiyun.com/ask/2020-10-12/971368555517115.png' />是[-a，a]上的奇函数; (2)若f(x)是奇函数，则<img src='https://img2.soutiyun.com/ask/2020-10-12/971368586317876.png' />是[-a，a]上的偶函数。

设函数f(x)在(0,+∞)内连续,f(1)=5/2,且对任何正数x和t,满足条件 <img src='https://img2.soutiyun.com/ask/2020-12-13/976721902069037.png' /> 则f(x)=().

设f(x)为连续函数,且f(0)≠0,则<img src='https://img2.soutiyun.com/ask/2020-12-13/976723029730536.png' />=().

A．A.0 B．B.π/16 C．C.π/2 D．D.π/3

设f(x)是以T为周期的周期函数,且f(x)在任意有限区间上连续,试证:对任意的a等式<img src='https://img2.soutiyun.com/ask/2021-01-14/979465028702515.png' />成立.

设函数f(t，x)在区域<img src='https://img2.soutiyun.com/ask/2020-08-26/96730758867009.png' /><img src='https://img2.soutiyun.com/ask/2020-08-26/967307611525398.png' />上连续，<img src='https://img2.soutiyun.com/ask/2020-08-26/967307604889018.png' />方程<img src='https://img2.soutiyun.com/ask/2020-08-26/967307617488739.png' />满足解的存在唯一性条件，其零解稳定，并且存在x₁＞0和x₂＜0使得分别由初值条件x(0)=x₁和x(0)=x₂确定的解当t-＞ +∞时都趋于零.证明方程的零解渐近稳定.

设f(x)为<img src='https://img2.soutiyun.com/ask/2021-02-02/981112914240121.png' />上以2π为周期，且具有二阶连续导数的函数, 记 <img src='https://img2.soutiyun.com/ask/2021-02-02/981112923970678.png' /> <img src='https://img2.soutiyun.com/ask/2021-02-02/981112932118144.png' />

设S(x)是周期为2π的函数f(x)的Fourier级数的和函数.f(x)在一个周期内的表达式为<img src='https://img2.soutiyun.com/ask/2020-12-22/977479036798748.png' />写出S(x)在[-π,π]上的表达式.

设x(t)的傅里叶变换为 <img src='https://img2.soutiyun.com/ask/2020-09-12/968751935866163.png' /> 并令 <img src='https://img2.soutiyun.com/ask/2020-09-12/968751959406509.png' /> (a)x(t)是周期的吗？ (b)x(t)*h(t)是周期的吗？ (c)两个非周期信号的卷积有可能是周期的吗？

设函数f(x,y)连续,<img src='https://img2.soutiyun.com/ask/2020-11-14/97418931389292.png' />其中R:z²+y²≤t²,求F´(t).

设f(x)为连续函数，又<img src='https://img2.soutiyun.com/ask/2020-12-20/977330361227981.png' />， 证明: (1)若f(x)为奇函数，则F(x)为偶函数. (2) 若f(x)为偶函数，则F(x)为奇函数.

A．必是奇函数 B．必是偶函数 C．不可能是奇函数 D．不可能是偶函数

设周期函数f(x)的周期为2π.证明: (1)如果f(x-π)=-f(x),则f(x)的傅里叶系数a₀=0,a_2k=0,b_2k=0(k=1,2,…); (2)如果f(x-n)=f(x),则f(x)的傅里叶系数a_2k₊₁=0,b_2k₊₁=0(k=0,1,2,…).