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sindhuja P Grade: 11
        

1.    Lt n→ ∞ sin 2  [π√((n!)2-n! )]


 


2.    Ltx→0 ({x})1/x + (1/x){x} ,  (x>0,{.} denotes fractional   part of x)


            please solve both the Questions.


 


                   

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear sindhu


first question


Lt n→ ∞ sin 2  [π√((n!)2-n! )]


or Lt n→ ∞ sin 2  [∏n!√( 1-1/n! )]


apply limit part inside the root will become 1


and n! is very large nimber but it is a even number.


so Lt n→ ∞ sin 2  [∏n!√( 1-1/n! )] = sin 2  [∏*even number]


                                                        =0


 


For second question


Ltx→0 ({x})1/x + (1/x){x}


 


as limit tends to zero {x}=x


  so Ltx→0 ({x})1/x + (1/x){x} =Ltx→0 (x)1/x + (1/x)x


   apply limit


      Ltx→0 (x)1/x + (1/x)x       = 0 +1=1





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Badiuddin



7 years ago
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