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Ask iit jee aieee pet cbse icse state board experts Expert Question: evaluate the limit
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wimbledon (0)

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Limx->0[n*sinx/x]+[n*tanx/x] 


where n belongs to the set of natural numbers and [.] denotes the greatest integer function


 

    
krishna.gopal (2686)

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when x tends to zero sin(x)/x is less than 1 while tanx/x is greater than 1. (At x = 0, sin(x) goes below y=x line while tan(x) goes above that line)
So answer is (n-1) + (n) = 2n-1

Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi
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