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Is the following limit well-defined?
limx-->∞ cot((x^(2)+1)/(x+3))
2 Answers
- Barry GLv 75 years ago
No. (x^2+1)/(x+3) --> x --> infinity. Since cot is a periodic function cot(infinity) cannot be determined. eg If x is an 'infinitely large' odd integer multiple of 90 degrees we would have cot(x) = 0. But if we add another 45 degrees to x we would still have an 'infinitely large' value for x, but now cot(x) would be -1. Adding another 45 degrees makes cot(x) infinite. So which answer is correct? All of them. None of them. It cannot be determined. The limit is not well-defined. It oscillates forever.
