# Bug in Limit in version 11.1.0

Bug introduced in version 11.1.0 and fixed in version 11.2.0

The infinite limit

Assuming[a>0&&b>0,
Limit[((1+a)*b*x)/Sqrt[1+(1+a)*b*x*((1+a)*b*x+Sqrt[1+(1+a)^2*b^2*x^2])],
x->Infinity]]


gives the correct result 1/Sqrt[2] on version 11.0.0 but gives the incorrect result 7/8 on version 11.1.0.

What exactly has changed and what are the pitfalls we need to be watching out for?

• I am getting the same thing with V11.1. – bobbym Mar 29 '17 at 8:21
• I get the same with versions 11.1.0 and 11.0.1 on Windows 7 x64. – Alexey Popkov Mar 29 '17 at 8:32
• Maybe it has something to do with assumptions. The limit Assuming[a>0, Limit[Sqrt[a^2+x^2]/Sqrt[1+(x*(x+Sqrt[a^2+x^2]))/a^2], x->0]] gives a on version 11.0.0 but gives Sqrt[a^2] on version 11.1.0. – Roman Mar 29 '17 at 9:46
• Will be fixed in a future release. Apologies for any trouble this may cause. It was a consequence of some code churn involving Series with fractional powers, on branch cuts. – Daniel Lichtblau Mar 29 '17 at 16:43
• @DanielLichtblau Despite this bug, I am very much happier with the way the new Series (in 11.1) handles branch cuts of logs and fractional powers. I look forward to further development of Series in future releases. – QuantumDot Apr 3 '17 at 17:36

Assuming[a > 0 && b > 0,