I am doing the 100 meter men's freestyle swimming lab (in case you know what I am referring to) and I need to fibd the lower limit analytically.
I am given a table of data containing the years after 1900 and the time in second of each country , for example:
Time. Country.
55.4 seconds. Australia
Year after 1900
56
And I first thought I would just set a limit, with something like , lim f(x)
X--》0
But my teacher said it couldn't be zero.
Plz help!!!
well lets think it might be like a hot stone cooling down to some room temperature Tf
Google Newton's law of cooling
T = Ts +(To-Ts)e^-(k t)
To is your original 1900 time
Ts is your final time in 2100 or whatever which is the fastest one can ever go
k is a constant that kind of fits your data points.
You can fool around with the values of k and how long it takes to reach the final record time Ts
to get a good fit with your data
To find the lower limit analytically for the 100 meter men's freestyle swimming lab, you need to analyze the data and determine the minimum time achieved by any country. The table of data you have provided contains the years after 1900 and the corresponding times in seconds for each country.
To begin, you should sort the data in ascending order based on the time column. This will allow you to easily identify the country with the lowest time.
Once the data is sorted, locate the country with the smallest time. This country represents the lower limit for the 100 meter men's freestyle swimming event. Note the time recorded for this country.
Now, to express the lower limit analytically, you can use a limit expression. However, your teacher mentioned that using zero is not allowed, so you will need to choose another value. You can pick a small positive value such as 0.001 as the value to approach in the limit expression.
Let's say the country with the smallest time is Australia with a time of 55.4 seconds. To represent the lower limit analytically, you can use the following limit expression:
lim (x→0.001) f(x)
Here, f(x) represents the time taken to complete the 100 meter men's freestyle swimming event. However, please note that you need to substitute the function f(x) with the equation or expression that corresponds to the swimming times. Without additional information about the specific equation or expression, I cannot provide a more accurate representation, but you can substitute the corresponding equation or expression in place of f(x) in the limit expression.
Remember to consult with your teacher or refer to any provided guidelines or materials for further information regarding the specific equation or expression you should use in the limit expression for the 100 meter men's freestyle swimming lab.