Reparamterizing, I think i got the answer but whats up with the t = 0?

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In summary, the author is trying to figure out how to reparameterize a curve and find the point (1,0,1), which is the solution to the problem.
  • #1
mr_coffee
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Hello everyone, Did i do this all right? I don't get what the point of this part is...
THe directions say, Reparameterize the curve r(t) which is listed on my image. With respect to arc elnth measured from the point (1,0,1) in the direction of incresing t. Well if u plug in t = 0, u will get the point (1,0,1), so what>? to make the problem correct, do i just have to note that somewhere? Here is my work and the final answer, is that acceptable? i can't see if I'm right or not and its just for studying for an exam. Thanks.
http://show.imagehosting.us/show/775217/0/nouser_775/T0_-1_775217.jpg
 
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  • #2
mr_coffee said:
Hello everyone, Did i do this all right? I don't get what the point of this part is...
THe directions say, Reparameterize the curve r(t) which is listed on my image. With respect to arc elnth measured from the point (1,0,1) in the direction of incresing t. Well if u plug in t = 0, u will get the point (1,0,1), so what>? to make the problem correct, do i just have to note that somewhere? Here is my work and the final answer, is that acceptable? i can't see if I'm right or not and its just for studying for an exam. Thanks.
http://show.imagehosting.us/show/775217/0/nouser_775/T0_-1_775217.jpg
I'm curious why you wrote:

[tex]s(t)=\int_0^t\sqrt{2}e^{t}\,du[/tex]

Did you mean dt? If so, then it should equal [itex]\sqrt{2}\left(e^t-1\right)[/itex].

Alex
 
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  • #3
Oh yeah my bad, sorry! hm..how did u get e^t-1? if [tex]sqrt{2}[/tex] is a constant, can't u just bring it out? and get... sqrt(2)[tex]\int[/tex]e^t? and isn't the integral of e^t just e^t?
 
  • #4
mr_coffee said:
Oh yeah my bad, sorry! hm..how did u get e^t-1? if [tex]sqrt{2}[/tex] is a constant, can't u just bring it out? and get... sqrt(2)[tex]\int[/tex]e^t? and isn't the integral of e^t just e^t?
Yes, but remember that you are integrating from u=0 to u=t. What is the value of e0? It isn't 0 like you assumed in your work :smile:

Alex
 
  • #5
ohh, t hanks again alex for the help...
so i'd get t = ln|s/sqrt(2) + 1|; do u know where the t = 0 comes in? or do i just state, t = 0?
 

Related to Reparamterizing, I think i got the answer but whats up with the t = 0?

1. What does it mean to "reparameterize" something?

Reparameterizing refers to the process of changing the way a variable is expressed or measured. This can involve converting units, transforming data, or using a different parameterization function. It allows for different representations of the same underlying data and can be useful in various scientific applications.

2. Why is reparameterizing important in scientific research?

Reparameterizing can help simplify complex data and make it easier to analyze and interpret. It can also reveal relationships between variables that may not have been apparent in their original form. Additionally, reparameterizing can make it easier to compare data across different studies or experiments.

3. How does reparameterization affect the interpretation of results?

Reparameterizing can change the values and units of variables, so it is important to consider how this may impact the interpretation of results. It is crucial to clearly document any reparameterization methods used in a study and to carefully interpret the results in the context of the chosen parameterization.

4. Can reparameterization affect the validity of a study?

In most cases, reparameterization does not affect the validity of a study as long as it is done carefully and with clear justification. However, it is important to consider the potential impact of reparameterizing on the study design and analysis, and to address any potential biases that may arise.

5. What does t = 0 mean in reparameterizing data?

The t = 0 point is often used in time series data to represent the starting point or baseline for a measurement. It can also be used in other types of data to represent a reference point or origin. When reparameterizing data, t = 0 may be shifted or redefined, so it is important to clearly define and communicate what it represents in the context of the study.

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