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lim(x rarr oo) (logx^(n)-[x])/([x]), whe...

`lim_(x rarr oo) (logx^(n)-[x])/([x])`, where `n in N` and [.] denotes the greatest integer function, is

A

1

B

(-1)

C

0

D

none of these

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The correct Answer is:
B
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. Let f(2)=4 and f'(2)=4. Then lim(xto2)(xf(2)-2f(x))/(x-2) is given b...

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  3. lim(x rarr oo) (logx^(n)-[x])/([x]), where n in N and [.] denotes the ...

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  4. Let f(a) = g(a) = k and their n^(th) order derivatives exist and are n...

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  5. Let f:R to R be a positive increasing function with lim(x to oo) (f(3x...

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  6. lim(x rarr 0) x^(2). sin (pi/x) is

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  7. If 0 lt x lt y, then lim(n rarroo)(y^(n)+x^(n))^(1/n) is equal to

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  8. The value of lim(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=

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  9. If f(x) = {((sin(1+[x]))/([x]), for [x] ne 0),(0, for [x] = 0):} , wh...

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  10. If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R, then lim(...

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  11. lim(x rarr 0) ((1-e^(x))sin x)/(x^(2)+x^(3)) =

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  12. lim(x rarr 0) (sqrt(1+x)-1)/x =

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  13. If f(x) = [((sin [x])/([x]), [x] ne 0),(0, [x] = 0)], then lim(x rarr ...

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  14. The value of lim(x rarr k^(-)) x -[x], where k is an integer, is

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  15. The value of lim(x rarr 0) (1-cos(1-cosx))/(x^(4)) is

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  16. lim(x rarr 3)[x] =

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  17. lim(x rarr 1) (x^(8)-2x+1)/(x^(4)-2x+1) =

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  18. If f(x) = sqrt((x-sinx)/(x+cos^(2)x)), then lim(x rarr oo) f(x) =

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  19. lim(n rarr oo) (1+(sin) a/n)^(n) equals

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  20. lim(x rarr 0) (4^(x)-1)/(3^(x)-1) =

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