LimitsHard
Question
Given a real valued function f such that
f(x) =
where [.] represents greatest integer function and {.} represents fractional part function, then
f(x) =
where [.] represents greatest integer function and {.} represents fractional part function, then
Options
A.
f(x) = 1
f(x) = 1B.
f(x) = cot 1
f(x) = cot 1C.cot-1
D.
f(x) = 1
f(x) = 1Solution
To find 
f(x)
L.H.L. =
f(x)
To findf(x)
L.H.L. =f(x)
R.H.L. =
f(x)
= 0
∵ L.H.L. ≠ R.H.L. so
f(x) does not exist. f(x) is not continuous at x = 0.
Now cot-1
= cot-1 (
)2 = cot-1 (cot 1) =1
f(x)L.H.L. =
f(x)To find
f(x)L.H.L. =
f(x)R.H.L. =
f(x)= 0
∵ L.H.L. ≠ R.H.L. so
f(x) does not exist. f(x) is not continuous at x = 0.Now cot-1
= cot-1 (
)2 = cot-1 (cot 1) =1Create a free account to view solution
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