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anonymous
 4 years 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
anonymous
 4 years 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

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0any guesses for this one?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0no guesses? i guess \(f(x)=x^2\)

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Just x^2? I thought it had to be more than that though

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the first simple point will be \(\frac{1}{n}\) the second will be \(\frac{2}{n}\) and the \(i\)th will be \(\frac{i}{n}\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then for each \(i\), \(f(\frac{i}{n})=\frac{i^2}{n^2}\)

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0multiply each by \(\frac{1}{n}\) and add the up you get \[\sum\frac{i^2}{n^3}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well don't be hoodwinked in to thinking these are all that easy usually it is much harder to tell

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0interesting, because the i and n values would be different right?
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