# Is it a bug in Limit?

Bug introduced in 9.0 and fixed in 10.0.0 and reintroduced in 11.2

Mathematica 9 on Windows and WolframAlpha says

Limit[Sin[Sqrt[x+1]]-Sin[Sqrt[x]],x->Infinity]


is Interval[{-2,2}]. But actually the limit is 0.

Limit[TrigFactor[Sin[Sqrt[x+1]]-Sin[Sqrt[x]]],x->Infinity]


gives 0 correctly.

• This is apparently a v9 bug. Version 8.04, 10.0.2, 10.1 and 10.2 all give 0. – Sjoerd C. de Vries Sep 20 '15 at 11:29
• I'm voting to close this question as off-topic because Bug introduced in 9.0 and fixed in 10.0.0 – user9660 Oct 28 '15 at 14:45
• @Lou I'd rather leave this for V9 users. – Kuba Oct 28 '15 at 16:08
• In v11.2, first limit has gone back to Interval[{-2, 2}] – Bob Hanlon Sep 17 '17 at 2:37
• Sorry about that. 11.3 should get it right again. – Daniel Lichtblau Sep 18 '17 at 16:47

Case closed but the topic should be left here for future visitors who use V9.

So:

Bug introduced in 9.0 and fixed in 10.0.0

• In the spirit of community and user-oriented, Thanks! – user9660 Oct 28 '15 at 17:05
• @Lou Thanks comrade :) – Kuba Oct 28 '15 at 17:10