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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

` lim _(x to 0) f (x)` is an integer

B

`lim _(xto0 ) f (x)` is non-integer

C

`f (x) ` has local maximum at `x=a`

D

`f (x)` has local minimum at `x=a`

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The correct Answer is:
A, D
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VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  2. If f(x)=(lim)(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where ...

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  3. Let f:R->R;f(x)={(-1)^n if x=1/(2^(2^n)), n=1,2,3.......... and 0 othe...

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  4. If lim(x->a) f(x) = lim(x->a) [f(x)] ([.] denotes the greatest intege...

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  5. let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} deno...

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  6. lim(x->0) (sin(sinx)-sinx)/(ax^3+bx^5+c)=-1/12 then

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  7. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

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  8. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

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  9. If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(s...

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  10. Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2 If lim(x->2) [f(x)] e...

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  11. A circular disk of unit radius is filled with a number of smaller circ...

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  12. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  13. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  14. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

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  15. A certain function f (x) has the property that f (3x)=alpha f (x) for ...

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  16. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  17. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  18. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

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  20. Ror the curve sin x+ sin y=1 lying in the first quadrant there exists ...

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