Primarygun Posted October 17, 2005 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?
TD Posted October 17, 2005 Posted October 17, 2005 It doesn't since the upper limit isn't equal to the lower limit (+ / - infinity).
Dave Posted October 17, 2005 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.
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