用数学归纳法证明:<img src='https://img2.soutiyun.com/ask/2021-02-22/982838635749578.png' />

与数学式子<img src='https://img2.soutiyun.com/shangxueba/ask/1515001-1518000/1515783/ct_cstccbm_ctccbchoose_00118(200912).jpg' />对应的C++语言表达式是

证明:对所有集合A,B和C,有<img src='https://img2.soutiyun.com/ask/2021-01-10/979154132976341.png' />

设z是任一复数,证明<img src='https://img2.soutiyun.com/ask/2021-01-13/9794048514659.png' />

证明“确定的原则”<img src='https://img2.soutiyun.com/ask/2021-01-09/979063969431976.png' />

试证明下列函数满足拉普拉斯方程：<img src='https://img2.soutiyun.com/ask/2019-06-18/929711665151155.png' />

利用分部积分证明:<img src='https://img2.soutiyun.com/ask/2021-01-25/980415524997009.png' />

设<img src='https://img2.soutiyun.com/ask/2020-12-15/976910006079741.png' />为同一区间上的可导函数,证明

如图3.10所示，在电荷体密度为ρ的均匀带电球体中，存在一个球形空腔。若将带电体球心O指向球形空腔球心O'的矢量用a表示，试证明球形空腔中任一点电场强度为<img src='https://img2.soutiyun.com/ask/2020-11-09/97380685115997.png' />

证明:若<img src='https://img2.soutiyun.com/ask/2020-11-11/973945141033851.png' />

证明柯特斯系数满足<img src='https://img2.soutiyun.com/ask/2020-08-04/965384831848618.png' />

利用Γ函数和B函数的关系，证明<img src='https://img2.soutiyun.com/ask/2021-01-19/979914972490034.png' />

证明:集合A是一个关系,当且仅当<img src='https://img2.soutiyun.com/ask/2021-01-10/979154705733101.png' />

设p＞1，证明不等式<img src='https://img2.soutiyun.com/ask/2021-01-18/979838709003026.png' />

与数学式子<img src='https://img2.soutiyun.com/shangxueba/ask/1887001-1890000/1889652/ct_ctcbm_ctcbchoosej_05667(20093).jpg' />应的C语言表达式是

证明不等式:<img src='https://img2.soutiyun.com/shangxueba/ask/51399001-51402000/51401966/977847325438542.png' />.

证明定理3:15中的等式<img src='https://img2.soutiyun.com/ask/2021-01-02/978463581870021.png' />

构造公式<img src='https://img2.soutiyun.com/ask/2020-12-17/97706736786159.jpg' />的否证，从而证明它是矛盾式。

用仪器测量某零件的长度n次，得到n个略有差别的数:a₁,a₂,…,a_n,证明:用算术平均值<img src='https://img2.soutiyun.com/ask/2020-12-20/977341497733953.png' />作为该零件的长度x的近似值，能使<img src='https://img2.soutiyun.com/ask/2020-12-20/977341503690294.png' />达到最小.

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' />

用真值表证明反演律:<img src='https://img2.soutiyun.com/ask/2021-01-21/980081620488771.png' />

证明不等式：<img src='https://img2.soutiyun.com/ask/2020-08-18/966606791867552.png' />

证明恒等式：<img src='https://img2.soutiyun.com/ask/2020-08-10/965923265077714.png' />

证明：若f为函数，则<img src='https://img2.soutiyun.com/ask/2020-08-12/966099742187747.png' />

证明:若<img src='https://img2.soutiyun.com/ask/2020-11-13/974144553195733.png' />