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# Tutor profile: Jason C.

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Jason C.
Tutor from MIT
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## Questions

### Subject:Python Programming

TutorMe
Question:

Write a function that takes two integers and returns their greatest common divisor.

Inactive
Jason C.

The greatest common divisor is at most the smallest of the two inputs. Therefore, we can just loop up to the minimum of the two inputs and check: $$\verb|def f(a, b):|$$ $$\verb| common_divisors = []|$$ $$\verb| for d in range(1, min(a, b) + 1):|$$ $$\verb| if a%d == 0 and b%d == 0:|$$ $$\verb| common_divisors.append(d)|$$ $$\verb| return max(common_divisors)|$$

### Subject:Pre-Calculus

TutorMe
Question:

Evaluate $$(1+i\sqrt 3) e^{-i \pi/3}$$.

Inactive
Jason C.

First, we will convert $$e^{-i \pi/3}$$ to rectangular form: $( e^{-i \pi/3} = \cos (-\pi/3) + i \sin (-\pi/3) = \frac{1}{2} - \frac{\sqrt 3}{2}.$) Then, we take the product of the two terms: (\begin{align*} (1 + i \sqrt 3) \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) &= \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) + i \sqrt 3 \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) \\ &= \frac{1}{2} - i \frac{\sqrt 3}{2} + i \frac{\sqrt 3}{2} + \frac{3}{2} \\ &= 2. \end{align*})

### Subject:Calculus

TutorMe
Question:

Evaluate $( \oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy],$) where $$C$$ is the boundary of the square with vertices $$(0, 0)$$, $$(1, 0)$$, $$(1, 1)$$, and $$(0, 1)$$, oriented counterclockwise

Inactive
Jason C.

By Green's theorem, we know that the integral about the boundary of region is equal to the integral of the divergence over the region. (\begin{align*}\oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy] &= \iint_{[0, 1]^2} \left[\frac{d}{dx}(x^2 + y^2) - \frac{d}{dy}(x^2 - y^2)\right] \,dA \\ &= \int_0^1 \int_0^1 [2x + 2y] \,dx\,dy = 2.\end{align*})

## Contact tutor

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## FAQs

What is a lesson?
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If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson.
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The content structure of the provided text is a series of tutoring profiles and questions with answers in various subjects, such as Python Programming, Pre-Calculus, and Calculus.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Enable contrast version

# Tutor profile: Jason C.

Inactive
Jason C.
Tutor from MIT
Tutor Satisfaction Guarantee

## Questions

### Subject:Python Programming

TutorMe
Question:

Write a function that takes two integers and returns their greatest common divisor.

Inactive
Jason C.

The greatest common divisor is at most the smallest of the two inputs. Therefore, we can just loop up to the minimum of the two inputs and check: $$\verb|def f(a, b):|$$ $$\verb| common_divisors = []|$$ $$\verb| for d in range(1, min(a, b) + 1):|$$ $$\verb| if a%d == 0 and b%d == 0:|$$ $$\verb| common_divisors.append(d)|$$ $$\verb| return max(common_divisors)|$$

### Subject:Pre-Calculus

TutorMe
Question:

Evaluate $$(1+i\sqrt 3) e^{-i \pi/3}$$.

Inactive
Jason C.

First, we will convert $$e^{-i \pi/3}$$ to rectangular form: $( e^{-i \pi/3} = \cos (-\pi/3) + i \sin (-\pi/3) = \frac{1}{2} - \frac{\sqrt 3}{2}.$) Then, we take the product of the two terms: (\begin{align*} (1 + i \sqrt 3) \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) &= \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) + i \sqrt 3 \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) \\ &= \frac{1}{2} - i \frac{\sqrt 3}{2} + i \frac{\sqrt 3}{2} + \frac{3}{2} \\ &= 2. \end{align*})

### Subject:Calculus

TutorMe
Question:

Evaluate $( \oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy],$) where $$C$$ is the boundary of the square with vertices $$(0, 0)$$, $$(1, 0)$$, $$(1, 1)$$, and $$(0, 1)$$, oriented counterclockwise

Inactive
Jason C.

By Green's theorem, we know that the integral about the boundary of region is equal to the integral of the divergence over the region. (\begin{align*}\oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy] &= \iint_{[0, 1]^2} \left[\frac{d}{dx}(x^2 + y^2) - \frac{d}{dy}(x^2 - y^2)\right] \,dA \\ &= \int_0^1 \int_0^1 [2x + 2y] \,dx\,dy = 2.\end{align*})

## Contact tutor

Send a message explaining your
needs and Jason will reply soon.
ContactÂ Jason

Start Lesson

## FAQs

What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.
user
The content structure of the provided text is a series of tutoring profiles and questions with answers in various subjects, such as Python Programming, Pre-Calculus, and Calculus.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS