Posted January 7, 2013 How would you go about with the following problems? What are the first steps? Share this post Link to post Share on other sites

Posted January 9, 2013 (Forgive any misuse of terminology here - I haven't formally taken this option yet, and all knowledge I have is from my own extended studies)I think what it's asking you to do here is find two series g(x) and h(x) - or, in this case, to use two sequences g(x) and h(x) which are definitions for f(x) where n>0 or n<1 respectively - prove that the limit of the nth term of both of those sequences has a limit as n approaches infinity at zero, show that the series are convergent, and show that for all x, g(x)<f(x)<h(x), and finally, since you have satisfied all the criteria to use the theorem, invoke the theorem to make the proof.For 2(a), it seems like it could be done using a similar method, just taking into account that the values of a*n and b are likely to be insignificant as n approaches infinity. However, it seems like a more difficult problem that would require careful manipulation to produce squeezing functions that use a and b and act as bounds for all a and b within their respective domains. 2(b) should follow from the case a=1, b=0.I've probably made a mistake somewhere in there, but I hope that gives you an idea where to start. Share this post Link to post Share on other sites