This was a problem from my calculus final a year ago that I've wanted to see for a while:
Use the delta-epsilon definition of a limit to prove that the limit as x approaches 0 of f(x) = sin(x)/(x^2 +1) is 0.
I tried using the squeeze theorem in an effort to bound sin(x), because I really don't know how to deal with sin(x) in a delta epsilon proof. This problem has just been on my mind for a while. Thanks for the help!
Can you show me how to do this proof? CB, what you wrote is true, but I'm not familiar with delta-epsilon proofs to know how to incorporate it into the rest of the proof.
You want d such that |x- 0| < d then |f(x) - 0 | < e
|f(x) - 0 | = | sin(x)/(x^2+1)| < |sin(x)|
take d = arcsin(e)
then if |x| < arcsin(e) then |sin(x)| < |sin(arcsin(e)| = e
But since then you can chose .
Originally Posted by Calculus26