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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)limf(x)` is an integer

B

`underset(xrarra)limf(x)` is non-integer

C

f(x) has local maximum at x=a

D

f(x) has local minimum at x=a

Text Solution

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The correct Answer is:
A, D
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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (More Than One Correct Option Type Questions)
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  7. If the maximum and minimum values of the determinant |(1 + sin^(2)x...

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  11. f(x)=sqrt(x-1)+sqrt(2-x)andg(x)=x^(2)+bx+c are two given functions suc...

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  13. For the function f(x)\ =\ 1n\ (1-1n\ x) which of the following d...

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  14. The function f(x)={:{(x+2,ifxlt-1),(x^(2),if-1lexle1),((x-2)^(2),ifxge...

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  15. A function f is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2...

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  17. Let f(x) be diferentiable function on the interval (-oo,0) such that...

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  18. If f:RrarrR(1)f(x) is a differentiable bijective function, then whic...

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  19. Let f:(0,oo)rarr(0,oo) be a derivable function and F(x) is the primiti...

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