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1. Lt n→ ∞ sin 2 [π√((n!) 2 -n! )] 2. Lt x→0 ({x}) 1/x + (1/x) {x} , (x>0,{.} denotes fractional part of x) please solve both the Questions.

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.


 


                   

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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Regards,
Askiitians Experts
Badiuddin


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