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Find a function f for which the limit below represents the area under f on the interval [0, a].
Here we assume the rectangles used have equal widths and right endpoints as sample points.
http://i49.tinypic.com/20ua7i9.jpg
 one year ago
 one year ago
Find a function f for which the limit below represents the area under f on the interval [0, a]. Here we assume the rectangles used have equal widths and right endpoints as sample points. http://i49.tinypic.com/20ua7i9.jpg
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.1
any guesses for this one?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
no guesses? i guess \(f(x)=x^2\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
on the interval \([0,1]\) divide the interval in to \(n\) parts each of length \(\frac{1}{n}\)
 one year ago

byerskm2Best ResponseYou've already chosen the best response.0
Just x^2? I thought it had to be more than that though
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the first simple point will be \(\frac{1}{n}\) the second will be \(\frac{2}{n}\) and the \(i\)th will be \(\frac{i}{n}\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
then for each \(i\), \(f(\frac{i}{n})=\frac{i^2}{n^2}\)
 one year ago

byerskm2Best ResponseYou've already chosen the best response.0
oh wow! Dang. I hate this notation. It makes it ten times more complicated than it needs to be.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
multiply each by \(\frac{1}{n}\) and add the up you get \[\sum\frac{i^2}{n^3}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
well don't be hoodwinked in to thinking these are all that easy usually it is much harder to tell
 one year ago

byerskm2Best ResponseYou've already chosen the best response.0
I have another one a lot like this. with a sqaure root. but I'm not sure about it
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
but the first clue should have been the \(i^2\) on the other hand if the interval had be \([1,2]\) it would have been completely different
 one year ago

byerskm2Best ResponseYou've already chosen the best response.0
interesting, because the i and n values would be different right?
 one year ago
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