Re: maths

Posted by Chocolate Frog on May 04, 2012; 6:42pm
URL: http://discussion-forum.276.s1.nabble.com/maths-tp7526962p7528225.html

AJ's solution is acceptable, of course, but a slightly different approach will make our lives even simpler. Notice that both n^(1/6) and n^(1/4) are greater than 1 for n > 1. So, their reciprocals will be less than 1. In symbols, u = n^(1/2) + n^(1/3) + n ^(1/4) < 3n^(1/2). Hence for n >= 9, u < n.

As for the DSE question, fn = n if x belongs to [0,1/n], and 0 otherwise. Limit fn as n tends to infinity exists everywhere except at x = 0. So, you're right, the answer should be (d).