简介：微积分对于工程师来讲，就像算数之于普通认生来讲是放我们的思想更加深刻有序。尝尝看看我们大学第一堂课程中的求解问题及其内容，renovate我们的活力。本文整理了上学期期末微积分考试试题，题量适中、考试点分布广泛。让我们回顾一下学习之后考核的快乐。在 期末微积分考试试题求解：利用python求解 中给出了部分求解答案。

关键词： 微积分，期末考试

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试题内容

目录
Contents

试卷内容

试题分析

试题总结

§01 试题内容

今天看到在“今日头条”上 清华大学期末微积分试卷，网友：不愧是清华的题，爱了爱了 有人给出了今年清华期末考试试题内容。

1.1 试卷内容

▲ 图1 试题第一部分

▲ 图2 试题的第二部分

1.2 试题分析

我们挑选一些题目来看看，先看第一部分的填空题

第1题和第2题，都是考察常微分方程的问题，显然第1题是可分离变量的常微分方程，所以我们只需要用分离变量法就可以求解了。对于第2题，是二阶齐次常微分方程，求通解我们可以构造特征方程，判断根的分布情况，从而得到对应齐次方程的通解。

第3题，属于基础常见函数极限计算题，这里可以通过积分的定义计算，我们只需要提出1/n，然后再利用0~1上的定积分即可。

第4题，考察分段函数的定积分。

第5题，考察泰勒公式的麦克劳林展开，将sinx＾3展开，注意计算不要错误。

第6题，求微分，相对而言就会稍微复杂一些。

第7题，求定积分，看似困难，但有个小技巧0-π上的∫xf（sinx）dx=π/2∫f（sinx）dx

接着后面的题考察的弧长微分、泰勒公式求极限……，隐隐感觉到了计算量的逐步上升。

看到这里，填空题似乎还可以接受，大都属于“基础题”，需要我们有一个牢靠的基础与扎实的计算能力，但是别忘了，这才第一部分的填空题，一个才3分。（瑟瑟发抖）。

第11题，讨论广义积分的收敛性，我们会发现这个积分既是无穷积分，也是瑕积分，所以我们需要分成两段分别去讨论，然后进行计算就可以了（不难但确实耗时间）。

第12题，写出对数列对应的函数，通过求导找出其驻点，从而得到极大值点再分析。

第13题，讨论函数的连续性、单调区间、极值点、凸性区间、拐点、渐近线等，都是比较基础的概念重要的事，但需要有耐心的去一个一个计算，计算量较大，对我们的熟悉度要求很高。

※ 试题总结 ※

微积分对于工程师来讲，就像算数之于普通认生来讲是放我们的思想更加深刻有序。尝尝看看我们大学第一堂课程中的求解问题及其内容，renovate我们的活力。本文整理了上学期期末微积分考试试题，题量适中、考试点分布广泛。让我们回顾一下学习之后考核的快乐。

在 期末微积分考试试题求解：利用python求解 中给出了部分求解答案，使用python帮助进行辅助求解。

■ 相关文献链接:

清华大学期末微积分试卷，网友：不愧是清华的题，爱了爱了

● 相关图表链接:

图1 试题第一部分
图2 试题的第二部分

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今年期末微积分考试试题：看看你能够在两个小时内做对几道题？

§01 试题内容

1.1 试卷内容

1.2 试题分析

※ 试题总结 ※

今年期末微积分考试试题：看看你能够在两个小时内做对几道题？相关推荐

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