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The value of lim(xrarrinfty)frac(x^3sin(...

`The value of `lim_(xrarrinfty)frac(x^3sin(1/x)-2x^2)(1+3x^2)`is

A

0

B

`-1/3`

C

`-1`

D

`-2/3`

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The correct Answer is:
B
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xrarrinfty)f(x)=

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  2. If lim(xrarrinfty)((x^2+1)/(x+1)-px-q)=0, then

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  3. The value of lim(xrarrinfty)frac(x^3sin(1/x)-2x^2)(1+3x^2)is

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  4. If f(x)={(sin[x]/[[x]], "for"[x] ne 0),(0, "for"[x] = 0):} where [x] d...

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  5. The number of points at which the function f(x)=1/log|x| is discontinu...

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  6. The function f(x)=(log(1+ax)-log(1-bx))/x is not defined at x =0. The ...

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  7. A function f(x) is defined as f(x)={((1-cos3x)/x^2, x ne 0),(b^2+4, x ...

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  8. If f(x)={((cosx)^(1/sinx),"for" x ne 0), (k, "for" x = 0):} The value ...

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  9. Points of discontinuities of the function f(x)=4x+7[x]+2log(1+x), wher...

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  10. The function f(x)=|x|atx=0 is:

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  11. g(x)=x|x|theng''(x)

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  12. The function defined by f(x)={((|x-3),, x ge 1), (1/4x^2-3/2x+13/4,, x...

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  13. If f(x)={((x-1)/(2x^2-7x+5), for x ne 1),(-1/3, for x=1):} then f(1)=

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  14. Let h(x)=max{-x,1,x^2} for every real x, then number of points of non-...

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  15. lim(nrarrinfty)(n^ksin^2n!)/(n+1)=0 for

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  16. If f(x)=sin(2pi[pi^2x])/(5+[x^2]) denotes the greatest integer functio...

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  17. If f(x)=|x-25| and g(x)=f(f(x)) then for xgt50, g'(x) is equal to

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  18. Let f(x)=[tan^2x], where [.]denotes the greatest integer function. The...

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  19. If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) ...

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  20. if f(x)=[sqrt2sinx], where [x] denotes the greatest integer function, ...

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