Question

Evaluate lim x tends to 2 fx if exist where fx={x-[x]}

Answer 1

HEYA!!

{ x } = x - [ x ]

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R.H.L

lt ( 2 + h ) - 2 [ 2 + h ]
h–>0

lt ( 2 + h ) - 2 [ 2 + 0 ]
h–>0

lt ( 2 ) - 2 ( 2 )

h–>0

= -2

L.H.L

lt ( 2 - h ) -2 [ 2 - h ]
h–>0

lt ( 2 - 0 ) - 2 [ 2 - h ]
h–>0

= 2 - 2 ( 1 )

= 2 - 2

= 1

L.H.L ≠ R.H.L

So,limit of this function at x = 2 doesn't exist.

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For

L.H.L

lt [ a - h ] = a - 1
h–>0

where [ ] is G.I.F