Nothing critical but your explanations on the domains were a bit unprecise to say the least. the "a quadratic is less than 0 between its two roots" is true in this case, but only because the coefficient of x2 is positive. if you have a quadratic with a negative leading coefficient, it is negative outside of the roots. The explanation for the second domain is as well lacking discipline. You can't just "change the -1 to 0". Since you are working in R, you can say that 0
This is not a criticism, rather it's a question. Why do you favour the form "y = whatever" as opposed to "f(x) = whatever"? I have always seen this written as f(x) or g(x) etc. and their derivatives as f'(x) g''(x) etc.
What is the name of the fancy 'L' the integral is equal to? Also, you can't use squares in greater or lesser than. -3 < 2 but it isn't true that (-3)^2 < (2)^2 = 9 < 4
Here is another example of y=(sin(x))^2. If you look at the function as y=sin(x), it ranges between -1 and 1. When you square the sine function, the range has to be in between 0 and 1 because (-1)^2=1, we cannot have some values that are less than 0 in that range. That's why we have to have values that are between 0 and 1.
I thought I'd seen most of the curves with nice arc lengths, but this is a new one!
Me too.
You are a good-looking guy. I'm sorry, I had to type that on a math channel.
Nothing critical but your explanations on the domains were a bit unprecise to say the least. the "a quadratic is less than 0 between its two roots" is true in this case, but only because the coefficient of x2 is positive. if you have a quadratic with a negative leading coefficient, it is negative outside of the roots. The explanation for the second domain is as well lacking discipline. You can't just "change the -1 to 0". Since you are working in R, you can say that 0
This is not a criticism, rather it's a question.
Why do you favour the form "y = whatever" as opposed to "f(x) = whatever"? I have always seen this written as f(x) or g(x) etc. and their derivatives as f'(x) g''(x) etc.
Just takes less space on my small board. I personally prefer f(x)
@@PrimeNewtons Thanks for taking the time to answer.
Terrific!
Fantastic job!
What is the name of the fancy 'L' the integral is equal to?
Also, you can't use squares in greater or lesser than.
-3 < 2 but it isn't true that (-3)^2 < (2)^2 = 9 < 4
1. I call it 'curly ell'.
2. Didn't he say that, about comparing squares? I thought he did.
Here is another example of y=(sin(x))^2. If you look at the function as y=sin(x), it ranges between -1 and 1. When you square the sine function, the range has to be in between 0 and 1 because (-1)^2=1, we cannot have some values that are less than 0 in that range. That's why we have to have values that are between 0 and 1.
Thanks Sir 👍
y=5-x/2 and the other side is 5-x
(5-x/2)^2+(5-x)^2=25
it is a straightforward problem,