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This has to be one of the hardest captcha tests I have ever seen. I think the answer is ln(2).
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You need to register to comment.That's because arctg(0) is zero and, even though you have the issue with sin 1/x, sin 1/x is always between -1 and 1; anything between -1 and 1 multiplied by zero is always zero.
Therefore you end up with ln(2) + ln(sqrt(0)) = ln(2).
arctan(0) is indeed zero, and zero multipled by sin(anything) = 0, but that means the limit becomes ln(2+sqrt(0)) = ln(2).
Your answer contains ln(sqrt(0)) which does not exist.