How do you find the limit of #xtan(1/(x-1))# as x approaches infinity?
The limit is 1. Hopefully someone on here can fill in the blanks in my answer.
The only way I can see to solve this is to expand the tangent using a Laurent series at
Multiplying by the x gives:
So, because all the terms apart from the first have an x on the denominator and constant on the numerator
because all terms after the first will tend to zero.