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).
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??
The example I gave was meant to be suggestive of how you could construct a rational sequence for
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:
Find a sequence converging 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 to be rational.