5 added 340 characters in body

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the fault of their officers. - Sun Tzu, The Art of War

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without prior definitions AND without prior instructions that it is up to the students to research the definitions?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations for these?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

• In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

• The class also has an unresolved issue about critical or inflection points, though the calculus student in question has yet to contact the professor, and they are on break for the upcoming weeek.

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the fault of their officers. - Sun Tzu, The Art of War

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without prior definitions AND without prior instructions that it is up to the students to research the definitions?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations for these?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the fault of their officers. - Sun Tzu, The Art of War

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without prior definitions AND without prior instructions that it is up to the students to research the definitions?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations for these?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

• In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

• The class also has an unresolved issue about critical or inflection points, though the calculus student in question has yet to contact the professor, and they are on break for the upcoming weeek.

4 added 18 characters in body; added 265 characters in body; deleted 10 characters in body

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the fault of their officers. - Sun Tzu, The Art of War

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without a prior definition anddefinitions AND without prior instructionsinstructions that it is up to the students to research the definitiondefinitions?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations for these?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without a prior definition and without prior instructions that it is up to the students to research the definition?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the fault of their officers. - Sun Tzu, The Art of War

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without prior definitions AND without prior instructions that it is up to the students to research the definitions?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations for these?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

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# Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without a prior definition and without prior instructions that it is up to the students to research the definition?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

# Are questions on overlapping solids of revolutions without prior definitions fair given that there are divided interpretations?

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without a prior definition?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like $$e^{iz} = \cos z + i \sin z$$, in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

# Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?

Situation:

I am helping a calculus student, and it seems the professor of the class has given a homework item on computing the volume and surface area of a solid revolution obtained by rotating a region about an axis that cuts the region's interior such that Pappus's centroid theorems don't apply. There are no prior examples in class discussions or class tutorials, and both the student and I are unable to find examples in Calculus by James Stewart or the student's textbook, Calculus by George B. Thomas.

The student has been told that a classmate has asked the professor about this, and the professor responded, 'There is nothing wrong with that item.'

Apparently, examples of these are very difficult to find, and according to the answer given in the question linked above,

'There is not an unanimous interpretation of what is the rotation solid in this case.'

My questions

1. Is this fair to give this to students without a prior definition and without prior instructions that it is up to the students to research the definition?

• For elementary maths: What elementary textbooks give definitions for situations like these?

• For advanced maths: What advanced textbooks discuss geometric, algebraic and physical interpretations?

• For maths education: What does the theory of teaching solids of revolution to beginning calculus students have to say in this case?

I should note

This isn't the first time the student has encountered a homework item without a definition.

In the semester prior to this, students were expected to compute the complex exponential $$e^z$$ in a homework item even though they had only the definition of $$e^{iy}$$, that is they were not told that $$e^{x+iy} := e^x e^{iy}$$. The student e-mailed the professor, who replied that the student was right that the students were not given this definition. This may seem like a small thing, but mistakes like this could lead to fallacies like because '$$e^{iz} = \cos z + i \sin z$$, $$Im(e^{iz}) = \sin z$$', in my opinion. (Obviously, complex analysis assumes calculus among others, so the class prior taught only complex variables, along with some probability and linear algebra, which had a little calculus but only up to what they knew in secondary school)

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