Nice job using all of the tools in your tool box to crank out the answer. However, using the third derivative to find critical numbers for the function to calculate K isn't going to work all for every case (or so I think). A better way to illustrate an example of calculating error bounds is to follow the mundane procedure and calculate K using the inequality formula, graphing whatever derivation of the function that yields K, or any other explicit method to actually get the point across. Furthermore, integral approximations are used to evaluate integrands that aren't integrable. I do believe your example is easily integrable. I was still foggy on finding K after watching this video. I get it now by just looking at the graph of the function. Thinking of K as magnitude also helped, but I'm no teacher.
1st- awesome job! and 2nd – how do you solve for K2 if the original function is . cos(x^2) it repeats so you cant really set it = to 0 and solve right? I found it by knowing the answer and solving for k2 backwards, but still how you solve for it? Thanks again!
how do you find k when the max of the function is 0 over the interval
i thought error bounds calculated as +/- 1/2T^1/2
What if the fourth derivative is not a constant? Do you find K by finding critical points like you did in the Trapezoidal example?
Nice job using all of the tools in your tool box to crank out the answer. However, using the third derivative to find critical numbers for the function to calculate K isn't going to work all for every case (or so I think). A better way to illustrate an example of calculating error bounds is to follow the mundane procedure and calculate K using the inequality formula, graphing whatever derivation of the function that yields K, or any other explicit method to actually get the point across. Furthermore, integral approximations are used to evaluate integrands that aren't integrable. I do believe your example is easily integrable. I was still foggy on finding K after watching this video. I get it now by just looking at the graph of the function. Thinking of K as magnitude also helped, but I'm no teacher.
You are very efficient and get right to the meat and potatoes of calculating error bounds.
thank you
You're missing the 8 when you took the 1st derivative
Thank u!!! Now it clear!
1st- awesome job!
and 2nd – how do you solve for K2 if the original function is . cos(x^2)
it repeats so you cant really set it = to 0 and solve right?
I found it by knowing the answer and solving for k2 backwards, but still how you solve for it? Thanks again!
He dropped the -8 but doesn't affect the problem
Great vid! Thanks!
lol I thought ik the only person that notice the missing 8
thank you
@grilledcheezuss right you are. Good thing that -8 derives to 0 in the second derivative and it doesn't effect the rest of the problem 🙂
i believe you're missing a -8 on the end of that first derivative.