这是Math 152， python in math的一次作业分析
1. Let $R$ be the region bounded by $y=x$ and $y=x e^{1-x / 2}$.
(a) Sketch the region $R$ and the line $y=3$.
(b) Find the exact and approximate volume of the solid formed by rotating $R$ about the $y$ -axis.
(c) Find the exact and approximate volume of the solid formed by rotating $R$ about the line $y=3$
此题是一个积分题，常规的思路是用fubini定理转化成单变量的积分然后通过计算得到结论，整个过程可以转化为python代码实现。由于这是Math 152这节课的前期内容，所以其实非常基础。
A spherical tank is $3 \mathrm{~m}$ tall and therefore has a capacity of about $14000 \mathrm{~L}$ (NOTE that $3 \mathrm{~m}$ is its diameter, and one cubic meter is $1000 \mathrm{~L}$ ). You have been asked to put level lines on the tank showing the depths where the tank contains 1000,5000 , and $10000 \mathrm{~L}$ of liquid.
(a) Use calculus to determine the height of each line (to the nearest $\mathrm{cm}$ ).
(b) Plot the circular cross-section of the tank and the level lines (NOTE the lines do not have to stay within the circle).
此题是一个简单的圆柱体体积计算题。
An elevator weighing 800 lbs is suspended by a 120 foot cable that weighs 10 lb per foot.
(a) Calculate the work done in moving the elevator from the ground floor to a height of 30
feet.
(b) Calculate the work done in moving the elevator from the ground floor to the top, i.e.,
the full 120 feet.
此题是一个重力做功的题，涉及到二次函数积分的计算。
4. Suppose the tank in $\# 2$ is full of water (weight density $9800 \mathrm{~N}$ ). Find the work required to pump all the water out of the tank…
(a) …if the tank is full.
(b) $-(\mathrm{d})$… if the tank is at each of the level lines calculated in #2.
第二题引发的一个做功的问题，本质上仍然是一个具有简单形式的函数的积分的计算。
Math 152的题目并不算难做，只要上课听懂，做起来准确率和效率都会时非常高的，如果实在需要帮助，也欢迎联系我们。
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关于math 152的更多内容请参阅一份Math152代写.
统计代写可以参考一份线性代数代写案例
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