Monday, 22 April 2013

limit of cosxtanx



As far as I know, 0 is not an indefinite form and it goes to zero. Then the limit of (cosx)tanx when x goes to π/2 should equal 0.




But after log transformation, its limit is . I am not sure which one is correct, zero or infinity?



Thanks for your help.



I slightly changed the question. I realized that x goes to π/2 (left hand limit) in the original question.


Answer



Suppose that f and g are functions such that as xa, f(x)0 and g(x), and consider h(x)=f(x)g(x). We know that
limxalnh(x)=limxag(x)lnf(x)=,
Thus,
limxah(x)=0.


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