# 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
148 Points
14 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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