讨论下列无穷积分的收敛性.
<img src='https://img2.soutiyun.com/ask/2021-02-05/98138654039982.png' />
时间:2024-04-13 09:24:18
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最先明确定义无穷级数收敛性的数学家是(),他是()。
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()首先给出了微积分无穷级数收敛性的判别法。
A、丹尼尔·伯努利
B、奥古斯丁·路易·柯西
C、雅各布·伯努利
D、路易吉·圭多·格兰第
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讨论下列积分的收敛性:
<img src='https://img2.soutiyun.com/ask/2021-01-25/980436331788089.png' />
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讨论反常积分λ取何值时绝对收敛或条件收敛.
讨论反常积分<img src='https://img2.soutiyun.com/ask/2020-11-30/975594851517965.png' />λ取何值时绝对收敛或条件收敛.
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讨论下列级数的收敛性。收敛的话,试求出级数之和.
<img src='https://img2.soutiyun.com/ask/2021-01-27/98061316284515.png' />
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证明:若无穷积分绝对收敛,函数φ(x)在[a,+∞)单调有界,则无穷积分收敛.
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.
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判别下列广义积分的收敛性:
<img src='https://img2.soutiyun.com/ask/2020-08-19/9666965590397.png' /><img src='https://img2.soutiyun.com/ask/2020-08-19/966696565618076.png' /><img src='https://img2.soutiyun.com/ask/2020-08-19/966696572187452.png' /><img src='https://img2.soutiyun.com/ask/2020-08-19/966696579021843.png' />
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讨论下列瑕积分的收敛性:
<img src='https://img2.soutiyun.com/ask/2021-02-05/981387122661124.png' />
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证明:0<λ<1,无穷积分都条件收敛.
证明:0<λ<1,无穷积分<img src='https://img2.soutiyun.com/ask/2020-11-13/974141104841498.png' />都条件收敛.