Alright, just had my Calc II final today, and there were two questions I wasn't too sure of.
The first: ∫ ln(x)/(x^(1/2)) on the interval of 0 to 1 - does it converge? I'm fairly certain that l'hopitals' doesn't work here, as plugging in 0 would give negative infinity over 0. If it does converge, the definite integral should be around -4 if I did my math correctly.
The second problem: does the sequence (1 + 3/n)^2n converge? If so, what value does it converge to? I wasn't sure how to approach this one, though I figured that the number in the parenthesis is always going to be > 1, therefore raising it to an increasing power will give a number that doesn't converge...although as the sequence continues on it will head towards 1... heh I think I might have answered my own question there, I must've been thinking of series while doing the problem at first.
2007-12-13
03:22:19
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3 answers
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Anonymous
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Mathematics