If ƒ(x) = cos 
cos 
; where, [ ] denotes the greatest integer function, then ƒ(x) is continuous at-
Text Solution
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(b, c)
Since, ƒ(x) = cos 
cos 
(given)
⇒ f(x) = cos 
sin 
Case I : OPTION
At x = 0, ƒ(0) is not defined
∴ ƒ(x) is discontinuous at x = 0
Case II : OPTION At x = 1, we have
LHL = 
cos 
sin 
⇒ LHL = 
cos 
sin 
⇒ LHL = 
cos [ π + ] cos 
∴ LHL = cos 3
Also, RHL = 
cos 
sin 
⇒ RHL = 
cos 
sin 
⇒ RHL = 
cos [ π – ] cos 
∴ RHL = cos 3
Also, f(1) = cos [ π ] sin 
= cos 3
Since, at x = 1, LHL = RHL = V
∴ function is continuous at x = 1
Similarly, the function is also continuous at x = 2.
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