若函数f（x）=（cos3x）/3-acosx在x=π/6处取得极值，则a的值为（）

A . f（x）在X=X 处的值一定存在且等于极限值 B . f（x）在X=X 处的值一定存在但不一定等于极限值 C . f（x）在X=X 处的值不一定存在 D . 如果f（x）在X=X 处的极限存在，则一定等于极限值

A . 半正定 B . 正定 C . 半负定 D . 负定

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' />

证明:若函数f(x)在[0,1]可导,且f(0)=0,<img src='https://img2.soutiyun.com/ask/2020-11-11/973975609415542.png' />有|f´(x)|≤|f(x)|,则f(x)=0,x∈[0,1].

A．-sin3x B．-3sin3x C．sin3x D．3sin3x

是 否

证明:若函数f(x)＞0,在[a,b]可积,令<img src='https://img2.soutiyun.com/ask/2020-11-13/974108578848118.png' />则 <img src='https://img2.soutiyun.com/ask/2020-11-13/974108619490443.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.

A．单调减少,曲线是凹的 B．单调增加,曲线是凹的 C．单调减少,曲线是凸的 D．单调增加，曲线是凸的

若函数f(x)在[a,b]上可积，证明存在折线函数列<img src='https://img2.soutiyun.com/ask/2021-01-22/98018065819823.png' />

B、f(x)在点x0处可能不连续 C、点x是f(x)的驻点 D、f(x)在点x0处不可导

证明:若函数f(x)在[a,b]单调增加,则 <img src='https://img2.soutiyun.com/ask/2020-11-12/974060207561962.png' />

证明:(1)若函数f在[a,b]上可导,且f'(x)≥m,则 <img src='https://img2.soutiyun.com/ask/2021-02-04/98128598322409.png' /> (2)若函数f在[a,b]上可导,且 <img src='https://img2.soutiyun.com/ask/2021-02-04/981285989538451.png' /> (3)对任意实数x₁,x₂,都有 <img src='https://img2.soutiyun.com/ask/2021-02-04/981286001647143.png' />

证明:若函数f(x)在区间I连续,且对任意有理数x∈I,有f(x)=0,则<img src='https://img2.soutiyun.com/ask/2020-11-11/973956935040429.png' />

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.