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The value of lim(x rarr 0) (e^(x)-e^(sin...

The value of `lim_(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=`

A

(-1/2)

B

(1/2)

C

1

D

(3/2)

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

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

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

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

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

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

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

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

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

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

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

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

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  16. The value of lim(n rarr oo){1/1.3+1/3.5+1/5.7+...+1/((2n+1)(2n+3))} is

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  17. The valueof lim(x rarr 0) (e^(ax)-e^(bx))/x is

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  18. If S(1) = sumn, S(2) = sumn^(2), S(3) = sumn^(3) then lim(n rarr oo) (...

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  19. The value of lim(x rarr 0) ((4^(x)-1)^(3))/(sin(x^(2)/4) log (1+3x)) ...

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  20. lim(x rarr 0) x log(e) (sinx) is equal to

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