A community for students.
Here's the question you clicked on:
 0 viewing
blackstreet23
 one year ago
Picture Problem using Simpson's Rule
Using Simpsons Rule (n = 8) , approximate an integral
blackstreet23
 one year ago
Picture Problem using Simpson's Rule Using Simpsons Rule (n = 8) , approximate an integral

This Question is Closed

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0Where can I post pictures ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle {\rm Simpson's~Rule} \\[0.9em] {\rm Area~~of~f~~over~~[1,3]~~with~n=8}~\\[1.9em]~\displaystyle \normalsize \frac{31}{8}\left(f(1)+4f(1.25)+2f(1.50)+4f(1.75)+2f(2) \\ +4f(2.25)+2f(2.50)+4f(2.75)+f(3)\right) }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2then the maximum error formula is \(\large\color{black}{ \displaystyle {\rm E}_{S}=\frac{ k(ba)^5 }{180n^4} }\) where k is the bound on the 4th derivative.... (if you want this one)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@blackstreet23 @solomanzelman Do you have everything you need to finish all four parts of the problem?

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0No I am stuck at part b

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Did you try @SolomonZelman 's formula? (you must have seen that before)

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0I mean I know that maximum points in a closed interval picture occur at critical points and end points. so do I need to take the fifth derivative ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0isn't the 4th derivative given? (you don't need 5th derivative )

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0i need the highest point of the fourth derivative and extrema occur at end points and critical points.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I see... The fifth derivative doesn't look too easy to guess highest you could differentiate the 4th derivative to find the 5th derivative

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0but that is correct right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I see... The forth derivative doesn't look too easy to guess highest *

freckles
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=f%28x%29%3D3%285x%5E460x%5E2%2B10%29%2F%2816%28x%5E2%2B1%29%5E%2815%2F4%29%29+x%3D10+to+10+and+y%3D1+to+1 beautiful finally figured out how to play with zooming options

freckles
 one year ago
Best ResponseYou've already chosen the best response.0notice the max is just under 1 for approximately what x value does that occur the 4th derivative is even (doesn't matter if you choose the positive or negative version of this particular number )

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0but the fifth derivative is still necessary just to show work right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0I would graph and estimate the max. instead of going through the 5th derivative AND solving the resulting equation for f5(x)=0. Generally the actual error is very much lower than the upper bound estimate, so numerically, it should be ok.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Graphically, it looks like to be at x=0.8. Poking around with a few iterations give x=0.787, and f4(.787) around .7149. That should solve part D. For part C, you don't need the relative max.

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0but because those values are not within the interval i do not need to worry of them until part d right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Exactly. For part B, the maximum is at x=1, and it's a strictly decreasing function, so no need to find the relative maximum.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0For part D, even a few casual guesses will give you the maximum within 3 decimal digits. Have you done part C (find the value of n)?

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0on d the new value of K4 will be 0.7149345503 right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0For part C, I have 10.1 or 10.2, which is kind of awkward, because it will bring the n=12 when we know almost sure that even n=10 may be good. Yes, the value of \(k_4\) is 0.7149 at about x=0.79.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Correction: Yes, I have n=5.713 => 6 for part C. I must have used the error bound ten times less when I calculated yesterday.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.