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If lim(xrarra) f(x)=lim(xrarra) [f(x)] (...

If `lim_(xrarra) f(x)=lim_(xrarra) [f(x)]` ([.] denotes the greates integer function) and f(x) is non-constant continuous function, then

A

`underset(xrarra)(lim)` f(x) is an integer

B

`underset(xrarra)(lim)` f(x) is non-integer

C

f(x) has local maximum at x = a

D

f(x) has local minimum at x = a

Text Solution

Verified by Experts

The correct Answer is:
A, D
We have `underset(xrarra)(lim)f(x)=underset(xrarra)(lim)[f(x)]`.
The can occur only when `underset(xrarra)(lim)f(x)` is an integer.
`rArr" "f(a^(+))gt f(a) and f(a^(-))gt f(a)`
`rArr" "x = a` must be point of local minima.
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