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underset(x to 0)"Lt" {1/x-(log(1+x))/(x^...

`underset(x to 0)"Lt" {1/x-(log(1+x))/(x^(2))}=`

A

0

B

1

C

`(1)/(2)`

D

`(-1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-LIMITS-PRACTICE EXERCISE
  1. underset(n to oo)lim (1+a+a^(2)+.....+a^(n-1))/(1+b+b^(2)+...+b^(n-1))...

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  2. The values of constants a so that underset(x to oo)lim ((x^(2)+1)/(x...

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  3. underset(x to 0)"Lt" {1/x-(log(1+x))/(x^(2))}=

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  4. Lim(x to 0) [(1)/(h""^(3)sqrt((8+h)))-(1)/(2h)]=

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  5. If Lt(x to 0) [1+x log(1+b^(2))]^(1//x)=2b sin^(2)theta, b gt 0 and th...

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  6. Lt(x to a) (2-(x)/(a))^("tan"(pix)/(2a))=

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  7. Lt(x to oo) (((n)/(n+1))^(lambda)+"tan"(1)/(n))^(n)=

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  8. Let f:R to R be such that f(x)=3 and f'(1)=6 then Lt(x to 0)((f(1+x))...

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  9. If underset(x to 0)"Lt" (1+a/x+b/x^(2))^(2x)=e^(2), then the value of ...

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  10. Lt(x to 0)(1+3sin^(2) sqrt(x))^(1//5x)=

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  11. Lt(x to 0) (e^(1//x))/(1+e^(1//x))=

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  12. f(x)={{:(x^(2),if x le 1),(x, if 1 lt x le 2),(x-3,if x gt 2):} then L...

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  13. Lt(x to 0)(cotx)^(sinx)=

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  14. Lt(x to 0)log(cos x//2)cosx=

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  15. Lim(x to 0){"cos"((x)/(2))cos((x)/(4))cos((x)/(8))....cos((x)/(2^(n)))...

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  16. If [x] denotes greatest integer function then Lt(x to0)(sin[cosx])/(1+...

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  17. Lt(x to 0)(sin^(-1)x+3x)/(tanx+2sin((1)/(2)sin^(-1)x)[3-4"sin"^(2)((1)...

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  18. Lt(x to 0)((a(1)^(x)+a(2)^(x)+...+a(n)^(x))/(n))^(1//x)=

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  19. Statement-I Lt(x to0)(tan{[-pi^(2)]x^(2)}-[pi^(2)]x^(2))/(sin^(2)x)=0 ...

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  20. If y=(1)/(2)sin^(-1)((2xy)/(x^(2)+y^(2))) and y lt x then Lt(y to 0)=

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