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Iff(x)={x+1/2, x<0 2x+3/4,x >+0 , then [...

If`f(x)={x+1/2, x<0 2x+3/4,x >+0` , then `[(lim)_(xvec0)f(x)]=` (where [.] denotes the greatest integer function) a. b. c. does not exist d. none of these

A

2

B

4

C

5

D

none of these

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VIKAS GUPTA (BLACK BOOK) ENGLISH-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  2. Let f (x) =x + sqrt(x^(2) +2x) and g (x) = sqrt(x^(2) +2x)-x, then:

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  5. 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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  6. If underset(xrarra)(lim)f(x)=underset(xrarra)(lim)[f(x)] ([.] denotes ...

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  7. Let f(x)=(sin^(-1)(1-{x})xxcos^(-1)(1-{x}))/(sqrt(2{x})xx(1-{x})), whe...

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  8. L=underset(xrarr0)(lim)(sin(sinx)-sinx)/(ax^(5)+bx^(3)+c)=-(1)/(12) ...

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

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

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

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  12. 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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  13. Iff(x)={x+1/2, x<0 2x+3/4,x >+0 , then [(lim)(xvec0)f(x)]= (where [.] ...

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

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  16. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

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  17. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

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  18. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

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

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

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