Science & Mathematics - 10 September 2007

Suppose the real valued f is unbounded in a neighborhood of a but its improper Riemann integrable exists anyway over the compact interval [a, b]. (A typical example is f(x) =1/sqrt(x) in [0,1], no matter the definition of f at 0). Let P_n be a sequence of partitions of [a, b] such that the norm of P_n (length of its largest interval) goes to 0 as n --> oo. Let S_n be a sequence of Riemann sums corresponding to P_n. Then, is it true that lim S_n = Integral a^b f(x) dx.

If f were bounded the answer would sure be yes, but since we have improper integrals I'm not sure.

Thank you for any help.

2007-09-10 04:58:48 · 2 answers · asked by Steiner 7 in Mathematics

2007-09-10 04:58:10 · 8 answers · asked by Chris B 1 in Weather

Well, when you apply electrolysis, you often add some other substances to lower the melting point of the reactant,

But adding salt to ice can makes ice melts slowly, right?

I wonder why. Could anyone please help me?

2007-09-10 04:58:04 · 3 answers · asked by Anonymous in Chemistry

Using the Pythagorean Theorem calculate the value of x it the side measure b=^2 and c=25^2
a) 7
b) 13
c) 12
d) 4

2007-09-10 04:56:23 · 10 answers · asked by Anonymous in Mathematics

Two forces act on a 3.1 kg mass, which undergoes acceleration a = 0.93 i - 0.22 j m/s2. If one of the forces is F1 = - 1.0 i - 2.9 j N, what is the other force?

2007-09-10 04:51:43 · 2 answers · asked by wil 1 in Physics

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2007-09-10 04:31:45 · 6 answers · asked by Frank Heyes 2 in Zoology

In past, people tried very hard to measure the orbit of planets based on observation, math and geometry without much accuracy. Nowadays, can our Science technology measure the orbit of planets accurately enough for a long period? The orbit of planets are affected by other planets with different weighting in 3-D, and there are many unknown planets in Universe, which cause any unknown gravity forces from a unknown distance. With current Science technology, do we simply predict the orbit of planets within a limited period [such as 100 years] by fitting an existing orbit of each planet? [Curve Fit] If any error occurs, then do we simply make some adjustment on existing curve of orbit? I would like to know what kinds of Science Technology we currently have to track the orbit of planets accurately. Do we have a true formula to measure the orbit of planets accurately for the next million years? Could anyone tell me how to reply someone's answer for more interpretions on my post? Thank you

2007-09-10 04:26:34 · 3 answers · asked by Eric 2 in Astronomy & Space

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2007-09-10 04:20:44 · 12 answers · asked by Marlene D 2 in Biology

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2007-09-10 04:13:48 · 7 answers · asked by Anonymous in Weather

I know the formula is a^2+b^2=c^2 with a and b being legs and c being the hypotenuse. My question is why are the squares necessary? If everthing is squared, wouldn't that be the same as just a+b=c? I am so confused.

2007-09-10 04:05:09 · 11 answers · asked by Anonymous in Mathematics

...but does anyone know how this is made possible? Thanks.

2007-09-10 04:01:27 · 7 answers · asked by higherlovetx 5 in Astronomy & Space

I'm not asking for answers here, just how I set these up correctly to arrive at the answers. Thanks

1) x^3 = 15x^2 + 88x + 100 (3 solutions)

2) square root(x) + square root (x+1) = x (1 solution)

2007-09-10 03:57:17 · 4 answers · asked by Oztac 1 in Mathematics

14 + 10x squared = 7y squared ...Please explain why or why not this is a function..and how you came up with the answer..thanks.

2007-09-10 03:51:03 · 5 answers · asked by ALF 2 in Mathematics

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