Real Analyis/Advanced Calculus Questions?

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Show by example that, even though f and g fail to have limits at x, it is possible for f + g tohave a limit at x.

2006-11-27 16:21:38 · 3 answers · asked by MMM 1 in Science & Mathematics ➔ Mathematics

Let f(x) = sin (1/x) and g(x)=-sin (1/x). Neither f nor g have limits at 0, but [x→0]lim f(x) + g(x) is obviously 0.

2006-11-27 16:37:48 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋

Let f be a function which fails to have a limit at x, and let g=-f.

2006-11-28 00:38:29 · answer #2 · answered by Steven S 3 · 0⤊ 0⤋

I don't understand sorry.

2006-11-28 00:26:17 · answer #3 · answered by Lizzie 5 · 0⤊ 1⤋