LimitsHard
Question
Let f(x) = [x] + 
, where [ . ] denotes the greatest integer function. Then
, where [ . ] denotes the greatest integer function. Then Options
A.f(x) is continuous on R+
B.f(x) is continuous on R
C.f(x) is continuous on R - I
D.discontinuous at x = 1
Solution
f(x) = [x] + 
Curve of y = f(x) =
Method : II y = f(x) can be discontinuous only at x ∈ I
so we check continuity only at x = n ∈ I
f(n) = [n] +
= n + 0 = n
LHL (x = n) is
[n - h] + 
= (n - 1) + 1 = n
RHL (x = n) is [n + h] + 
= (n + 0) = n
f(x) is continous for x ∈ R
Curve of y = f(x) =
Method : II y = f(x) can be discontinuous only at x ∈ I
so we check continuity only at x = n ∈ I
f(n) = [n] +
= n + 0 = nLHL (x = n) is
[n - h] + = (n - 1) + 1 = n RHL (x = n) is
[n + h] + = (n + 0) = n f(x) is continous for x ∈ R
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