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Question: Answered & Verified by Expert
If fx=x-x4, x∈R, where x denotes the greatest integer function, then:
MathematicsLimitsJEE MainJEE Main 2019 (09 Apr Shift 2)
Options:
  • A limx→4+fx exists but limx→4-fx does not exist
  • B f is continuous at x=4
  • C limx→4-fx exists but limx→4+fx does not exist
  • D Both limx→4-fx and limx→4+fx exist but are not equal
Solution:
2907 Upvotes Verified Answer
The correct answer is: f is continuous at x=4

R.H.L.=limx→4+x-x4=4-1=3

L.H.L.=limx→4-x-x4=3-0=3

fx=4-1=3

L.H.L.=f4=R.H.L.

Hence, given function is continuous at x=4.

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