证明Dirichlet公式并由此证明其中f连续.

A . 一致 B . 互相垂直 C . 相反

A . A.一致 B . B.互相垂直 C . C.相反 D . D.不一致

设f(x)在区间[0,1]上连续，证明:<img src='https://img2.soutiyun.com/ask/2020-12-15/976873792952469.png' />

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' />

设f(x)在<img src='https://img2.soutiyun.com/ask/2021-02-02/981108508925152.png' />上连续，且<img src='https://img2.soutiyun.com/ask/2021-02-02/98110851624057.png' />，证明 <img src='https://img2.soutiyun.com/ask/2021-02-02/981108523349977.png' />

试利用结论“若f(x)可导，则当|x|很小时，有f(x)≈f(0)+f'(0)x"，证明下列近似公式。 (1)当|x|很小时，sinx≈x (2)当|x|很小时，ex≈1+x (3)设a＞0且|b|与a_n相比是很小的量，则 <img src='https://img2.soutiyun.com/ask/2020-08-17/966510793966516.png' />

证明：若随机变量F~F(k，m)，则当<img src='https://img2.soutiyun.com/ask/2020-08-04/965400230538372.png' />时，有 <img src='https://img2.soutiyun.com/ask/2020-08-04/965400253632693.png' /> 由此写出E(F)，Var(F).

A．一致 B．互相垂直 C．相反 D．不一致

证明:若f在[a,+∞)上一致连续,且<img src='https://img2.soutiyun.com/ask/2021-02-05/98138680072271.png' />收敛，则<img src='https://img2.soutiyun.com/ask/2021-02-05/981386807293086.png' />

设f(x)在[a,b]上连续,且a＜c＜d＜b,证明:在[a,b]上必存在点ξ 使<img src='https://img2.soutiyun.com/ask/2021-01-12/979304261428851.png' />其中m＞0,n＞0.

设函数<img src='https://img2.soutiyun.com/ask/2020-12-16/976976603992918.png' />,其中函数g(x)在(-∞,+∞)上连续,且 g(1)=5,<img src='https://img2.soutiyun.com/ask/2020-12-16/976976616554637.png' />,证明<img src='https://img2.soutiyun.com/ask/2020-12-16/976976676821084.png' />,并计算f''(1)和F'''(1).

设<img src='https://img2.soutiyun.com/ask/2021-01-28/980692750486118.png' /> (1)证明f(x)在[0,+∞)上可导，且一致连续; (2)证明反常积分<img src='https://img2.soutiyun.com/ask/2021-01-28/980692795149672.png' />发散。

证明曲面<img src='https://img2.soutiyun.com/ask/2021-01-29/980784359816037.png' />在任一点处的切平面都通过原点，其中函数f连续可微。

设f(x)在(-∞,+∞)上连续,证明 <img src='https://img2.soutiyun.com/ask/2020-12-16/976976920461019.png' />

设一元函数f(u)在[-1,1]上连续，证明 <img src='https://img2.soutiyun.com/ask/2021-02-01/981026749760827.png' /> 其中Ω为单位球<img src='https://img2.soutiyun.com/ask/2021-02-01/981026759890406.png' />。

对于<img src='https://img2.soutiyun.com/ask/2020-11-27/975335669580105.jpg' />的数值积分公式<img src='https://img2.soutiyun.com/ask/2020-11-27/975335683575906.jpg' />，其中P(x)为对f(x)在x=0，h，2h进行插值的2次多项式。证明：<img src='https://img2.soutiyun.com/ask/2020-11-27/975335713170598.jpg' />

证明Dirichlet函数<img src='https://img2.soutiyun.com/ask/2020-08-18/966606182624706.png' />在任何x∈R处的极限都不存在。

设u=u(x，t)是初边值问题 <img src='https://img2.soutiyun.com/ask/2020-07-27/964709812982683.png' /> 的解，其中常数b≥0，|p(t)|≤B，|q(t)|≤B，|f(x)|≤M.证明 <img src='https://img2.soutiyun.com/ask/2020-07-27/964709832611805.png' /> 并由此建立.上述初边值问题解的唯一性和对初值和边界数据的连续依赖性.

考虑下列修正的牛顿公式(单点Steffensen方法) <img src='https://img2.soutiyun.com/ask/2020-09-10/968583151416147.png' /> 设f(x)有二阶连续导数,<img src='https://img2.soutiyun.com/ask/2020-09-10/968583169623188.png' />试证明该方法是二阶收敛的.

A．一致 B．互相垂直 C．相反 D．平行