Evaluate the following limits,
where [ . ] represents greatest integer function and { . } represents fractional part function
(i) 
[sin x] (ii) 
(iii) 
sgn [tan x] (iv) 
sin –1 ( n x)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)0
(ii)Limit does not exist
(iii)Limit does not exist
(iv)0
Sol. (i) 
[sin x] By graph of sin x
R.H.L = 
[sin x] = 0 L.H.L. = 
[sin x] = 0 so 
[sin x ] = 0
(ii) 
R.H.L. = 
= 
= 
= 
= 0
L.H.L. = 
= 
= 
= 1
L.H.L. ≠ R.H.L.
so 
does not exist.
(iii) 
sgn [tan x]
L.H.L. = 
sgn [tan x] = 
sgn [tan ( π – h)] = 
sgn (– ve) = –1
R.H.L. = 
sgn [tan x] = 
sgn [tan( π + h)] = 
sgn (+ ve) = 0
L.H.L. ≠ R.H.L. so limit does not exist
(iv) 
sin –1 ( n x) = sin –1 
= sin –1 (0) = 0
so 
sin –1 ( n x) = 0
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