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If lim(x->a) f(x) = lim(x->a) [f(x)] ([...

If `lim_(x->a) f(x) = lim_(x->a) [f(x)]` ([.] denotes the greatest integer function) and `f(x)` is non-constantcontinuous 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

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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