need help in calculus

[kittycat]

having doubt plz help
lim x->0 [sin(abs(x))/x]

where abs is mod and [] denotes greatest function integer

for x-->0+ am getting 0
but for x-->0- how come it is -1

i know Limit won't exist getting it from 2nd method plz tell me
m confused
-_-

see limx->0- [-sinx/x] inside part should be lesser than 1 nah :O how come the value inside would be greater than 1 :O
if it greater than 1 then m getting answer but how it will be greater than 1 :'(

limx->0- [-sinx/x]

inside part sinx/x will be lesser than or greater than one ??????

 

[serds]

The graph of

looks like this:

 

[tkhunny]

From the right, you get this ==> 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 (for some sequence approaching zero and then finally arriving at zero.)

From the left, you get this ==> -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1 (for some sequence approaching zero and then finally arriving at zero.)

 

[DrPhil]

lim x->0 [sin(abs(x))/x]

where abs is mod and [] denotes greatest function integer

How is the [] operation defined for negative argument? If it is the next smaller integer, then [-epsilon] = -1.
If it is the smallest magnitude integer, then [-epsilon] = 0