Parameterize an intersection between a cylinder and plane z=0

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The discussion centers on the parameterization of the intersection between a cylinder and the plane z=0. Participants point out a discrepancy in the direction of rotation, noting that the arrows and equations appear counterclockwise despite claims of clockwise rotation. There is also a correction regarding the use of 'sen' instead of 'sin' due to language differences, with 'sen' being the Spanish term for sine. Clarifications are made regarding the correct substitution of values in the integral. Overall, the conversation highlights the importance of accurate notation and direction in mathematical representations.
xodaaaaax
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Homework Statement
Help with parameterize the intersection as shown in the figure
Relevant Equations
x^2+y^2=4 and z=0
Screenshot_1.png


Attempt.jpg
 
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You say that you are going clockwise, but your arrows and equations look counterclockwise.
Other than that, it looks ok to me. Shouldn't all those 'sen's be 'sin's?
 
FactChecker said:
You say that you are going clockwise, but your arrows and equations look counterclockwise.
Other than that, it looks ok to me. Shouldn't all those 'sen's be 'sin's?
Oh my bad i was copying my notes into that picture so that it would be easier to understand them and messed up those arrows, yes they should be going clockwise. anyways, i type "sen" because i speak spanish, sorry about that.

So those are the values i should substitute in that integral?
 
Your y(t) equation will make it go around counterclockwise.
 
FactChecker said:
Your y(t) equation will make it go around counterclockwise.
I think i get it now, thank you so much
 
xodaaaaax said:
anyways, i type "sen" because i speak spanish
... and "sin" en español means "without".
 
First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...