# Multivariable Calculus - midterm questions

• s8on95
In summary: For the "estimate the integral" problem, I do not understand why e(sinx cosx sinz) is considered a constant function.
s8on95
I have two problems I need help with

1. Homework Statement

https://ccle.ucla.edu/mod/resource/view.php?id=801511
https://ccle.ucla.edu/mod/resource/view.php?id=778704

2,3. Answers and work are givenIn the surface integral problem, I do not understand how it sets it up for Method 1. (How does it go from integral of x2+y2 to 2/3 integral of x2+y2+z2

For the "estimate the integral" problem, I do not understand why e(sinx cosx sinz) is considered a constant function.
Also, any cramming advice for passing a computation multivariable calc test would be appreciated.

Total integers, with symmetry limits have 2/3 ratio.

theodoros.mihos said:
Total integers, with symmetry limits have 2/3 ratio.

Could you explain that with more detail. The phrases total integers and symmetry limits do not appear in my textbook and google isn't much help.

Make integrations with independent variables.
$$\int_{-a}^{a}\int_{-a}^{a}\int_{-a}^{a}dxdydz \,\text{and}\, \int_{-a}^{a}\int_{-a}^{a}dxdy$$
They are for cube but the ratio is the same for symmetric integration limits. To make the 2nd integral directlly have much more work.

s8on95 said:
I have two problems I need help with

1. Homework Statement

https://ccle.ucla.edu/mod/resource/view.php?id=801511
https://ccle.ucla.edu/mod/resource/view.php?id=778704

2,3. Answers and work are given

In the surface integral problem, I do not understand how it sets it up for Method 1. (How does it go from integral of x2+y2 to 2/3 integral of x2+y2+z2
By symmetry, each of the following integrals gives the same value.

##\displaystyle \ \iint_{S} x^2\, dA=\iint_{S} y^2\, dA=\iint_{S} z^2\, dA\ ##

You will usually get better response if you can post the images of your work directly.

Better yet, is to use LaTeX OR all the nice little symbols PF has provided for you.

Thank you both, it makes sense.

## 1. What topics are typically covered on a Multivariable Calculus midterm?

A Multivariable Calculus midterm usually covers topics such as vector calculus, partial derivatives, multiple integrals, and applications of these concepts.

## 2. How should I study for a Multivariable Calculus midterm?

To study for a Multivariable Calculus midterm, it is important to review all the main concepts and formulas, practice solving problems from your textbook and class notes, and work through practice exams. It is also helpful to attend review sessions and seek help from your professor or classmates if you are struggling with any specific topics.

## 3. Are there any common mistakes to avoid on a Multivariable Calculus midterm?

Some common mistakes to avoid on a Multivariable Calculus midterm include not understanding the geometric interpretation of multivariable concepts, not being able to apply the correct formulas to solve problems, and making careless errors in calculations. It is important to carefully read and understand each question before attempting to solve it.

## 4. Will a Multivariable Calculus midterm be calculator-allowed?

It depends on the professor and the specific exam. Some professors may allow the use of calculators, while others may require students to solve problems by hand. It is important to clarify with your professor beforehand to know what to expect.

## 5. How much time should I allocate for a Multivariable Calculus midterm?

The amount of time needed for a Multivariable Calculus midterm can vary depending on the difficulty of the exam and your own understanding of the material. It is recommended to allocate at least 2-3 hours to thoroughly review and complete the exam, but it may take longer for some students.

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