Continuity and DifferentiabilityHard
Question
The function f(x) = [x] cos 
[.] denotes the greatest integer function, is discontinu ous at
[.] denotes the greatest integer function, is discontinu ous atOptions
A.all x
B.all integer points
C.no x
D.x which is not an integer
Solution
Here, f(x) = [x]cos
∴ f(x)
which shows RHL = LHL at x = n∈ Integer as if x = 1
⇒
cos 
π = 0
and
0 = 0
Also, f(x) = 0
Similarly, when x = 2
⇒
f(x) = 
f(x) = 0
Thus function is discontinuous at no x.
Hence,(c) is the correct ancwer.
∴ f(x)
which shows RHL = LHL at x = n∈ Integer as if x = 1
⇒
cos π = 0and
0 = 0Also, f(x) = 0
Similarly, when x = 2
⇒
f(x) = f(x) = 0Thus function is discontinuous at no x.
Hence,(c) is the correct ancwer.
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