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Can you find any sequence of rationals such that it converges to π/4?
use the fact that the rationals are dense in the reals,
or you can think about the decimal expansion of π/4. How can you get rational numbers out of that, rational numbers that converge to π/4?
Can anybody help me with this immediately??
use the fact that the rationals are dense in the reals to find the answer for this,,,
Let f:R→R be a continuous function such that f(q)=sinq for q∈Q (rational numbers). Find the value of f(π/4).
If the question was just asking aboutQuote:
Originally Posted by chath
, I'd suggest this rational sequence to you:
Etc.
no not about pi.i need a rational function that converges to pi/4
I have this idea...to find f(π/4) we need to pick a sequence xn→π/4 and investigate what f(xn) converges to....will that be ok for this???
The example I gave was meant to be suggestive of how you could construct a rational sequence forQuote:
Originally Posted by chath
Think about it a minute. Each of those, each term in the sequence, is rational, and their limit goes to
So can you think of a different-but-related sequence of rationals whose limit goes to
it sounds like you're thinking along these lines:Quote:
Originally Posted by chath
Find a sequenceconverging to
, and then
will converge to
If so, that isn't going to get you very far, because there's a complication with the function not having an inverse (though, by restricting domains, that can be delt with), and, vastly more intractable, you're going to need these