证明连续函数的局部有界性：若函数f（x)在点x₀处连续，则函数在点x₀的某邻域内有界。

A . 连续且可导 B . 连续且可微 C . 连续不可导 D . 不连续不可微

A . 2 B . -2 C . -1 D . 1

A . 间断 B . 连续 C . 第一类间断 D . 可能间断可能连续

证明:若函数f(x)在a连续,则函数 <img src='https://img2.soutiyun.com/ask/2020-11-11/973957882099598.png' /> 在a都连续.

证明:若函数f(x)在[O,+∞)连续,且<img src='https://img2.soutiyun.com/ask/2020-11-12/974063888799517.png' />则<img src='https://img2.soutiyun.com/ask/2020-11-12/974063900815204.png' />

若函数f(x)在点x=x₀处不可导，则曲线y=f(x)在点(x₀，f(x₀))处没有切线；

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。

证明:若函数f(x)在区间[a,+∞)上连续且有极限<img src='https://img2.soutiyun.com/ask/2020-12-13/976732708656138.png' />则(x)在区间[a,+∞)上是有界的.

是 否

证明:若函数f(x,y)在区域R连续,且对任意有界闭区域<img src='https://img2.soutiyun.com/ask/2020-11-14/974187340984076.png' />都有 <img src='https://img2.soutiyun.com/ask/2020-11-14/974187353662801.png' />

证明:若函数f(x)与φ(x)在[a,b]连续,则 <img src='https://img2.soutiyun.com/ask/2020-11-12/974060778329609.png' />

证明:若函数f(x)在(a,+∞)连续,且<img src='https://img2.soutiyun.com/ask/2020-11-11/97395757022676.png' />则f(x)在(a,+∞)有界.

证明:若函数y=f(x)在[a,b]严格增加,且连续则反丽数x=f^-1(y)在点a=f(a)右连续,即 <img src='https://img2.soutiyun.com/ask/2020-11-11/973957297199144.png' />

证明:若无穷积分<img src='https://img2.soutiyun.com/ask/2020-11-13/97414103002922.jpg' />绝对收敛,函数φ(x)在[a,+∞)单调有界,则无穷积分<img src='https://img2.soutiyun.com/ask/2020-11-13/974141041163856.jpg' />收敛.

A.<img src='https://img2.soutiyun.com/ask/2019-07-15/932037149907256.png' /> B.f(x)在点Xo的某个邻域内有定义 C.<img src='https://img2.soutiyun.com/ask/2019-07-15/932037165663284.png' /> D.<img src='https://img2.soutiyun.com/ask/2019-07-15/932037176630103.png' />

A．lim（x→xo+）f（x）=lim（x→xo-）f（x） B．lim（x→xo）f（x）=f（xo） C．f（x）在点xo的某个邻域内有定义 D．lim（x→xo+）f（x）=f（xo）

设f(x)是[a,b]上的有限函数,若存在M＞0,使对任何ε＞0都有<img src='https://img2.soutiyun.com/ask/2020-08-13/966171531356788.png' /><img src='https://img2.soutiyun.com/shangxueba/ask/50574001-50577000/50574553/spacer.gif' /> 则f(x)是[a,b]上有界差函数.

设函数f在点x=1处二阶可导,证明:若f'(1)=0,f"(1)=0,则在x=1处有<img src='https://img2.soutiyun.com/ask/2020-11-28/975441569605878.png' /> <img src='https://img2.soutiyun.com/ask/2020-11-28/97544157767434.png' />

若函数u=ϕ(x)在点x=x₀处可导,而y=f(u)在点<img src='https://img2.soutiyun.com/ask/2021-01-13/979382799101577.png' />处不可导,则复合函数y=f[ϕ(x)]在点x0处必不可导.()

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.