Primarygun Posted October 17, 2005 Share Posted October 17, 2005 lim x-->0 [(1/x)+x] Can I split it into limx-->(1/x) + limx--->0 (x)? A principle said it can if both of the functions exist. But does the former exist? Link to comment Share on other sites More sharing options...
TD Posted October 17, 2005 Share Posted October 17, 2005 It doesn't since the upper limit isn't equal to the lower limit (+ / - infinity). Link to comment Share on other sites More sharing options...
Dave Posted October 17, 2005 Share Posted October 17, 2005 Indeed. If you know that [imath](a_n) \to a, (b_n) \to b[/imath] then it's fairly easy to prove that [imath](a_n + b_n) \to a+b[/imath]. Doesn't work if one of the limits is undefined though. Link to comment Share on other sites More sharing options...
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