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Hey gang. Another quick question. Can anyone remind me how you would find a vector in a particular subspace that is CLOSEST to a function.
The exact question is to find the vector in U closest to cos (t).
The orthonormal basis of the subspace is (1), (t-1), (t^2-4t+2), (t^3-9t^2+18t-6), and (t^4-16t^3+72t^2-9t+36)
I've just spent so much time getting that basis, and would appreciate any help in leading me in the right direction. I'll do the work if someone can tell me the process. Thanks so much!!!!
Thank you a million times. You made it very easy to understand.
When you told me to split the integral earlier, I plugged it into Maple and it spat out an answer, so I thought "job well done" and left it to go for breakfast. Now that I've come back to it, I see that the answer involves a fresnel function and that I was premature in my elation. So I'm open to further advice. I'm not quite clear on what you are suggesting in your follow up. I'm going to look into the Newton-Cotes formula.
The exact question asks us to use ten trapezoids to approximate the given integral. The only prerequisite for the question is that we have knowledge of calculus up to Taylor Series.
I'm sorry if I am being dense, but I'm admittedly weak in this area. Thanks for your patience!
Ah, right in front of my face! Thanks so much for your help!
I HAVE to use the trapezoid rule, and if by subtracting off the singularity you mean change the limit of integration, I'm not allowed to do that. The function to be integrated is:
(cos(x)dx)/sqrt(x)
from 0 to pi/2
Thanks for the help!
Hello again. Another question I've been struggling with (though it probably should be cake) is how to apply the trapezoid rule for area under a curve when the left side of the function is undefined (goes up to infinity). I'm not allowed to change the limit of integration. The problem comes, obviously, when trying to compute one of the bases of the left-most trapezoid. As the function is undefined at that point, I don't know how to get a value. Hope this question makes sense- I've no formal training in this topic, and can't find information on the topic. Thanks!
Thanks. I was thinking about a Taylor Series, but didn't think to center it around one. I don't know if this is what he's looking for, but it's the best advice I've gotten so far!
Hey y'all. I've been asked to make the best approximation ln(2) using only the four operations on a primitive calculator. (+,-,÷, ×)
That is the entire question, there are no other clues as to how I might start or in what direction I should take the problem. Any ideas? Thanks for the help!
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