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Lt(x to oo) (sqrt(x))/(sqrt(x+sqrt(x+sqr...

`Lt_(x to oo) (sqrt(x))/(sqrt(x+sqrt(x+sqrt(x))))=`

A

1

B

`oo`

C

`(1)/(2)`

D

`(1)/(sqrt(2))`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-LIMITS-EXERCISE-II
  1. Lt(x to oo) ((x+1)^(10)+(x+2)^(1)....+(x+50)^(10))/(x^(10)-10^(10))

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  2. underset(x to oo)lim (sqrt(x^(2)+1)-root3(x^(2)+1))/(root4(x^(4)+1)-ro...

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  3. Lt(x to oo) (sqrt(x))/(sqrt(x+sqrt(x+sqrt(x))))=

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  4. Lt(x to oo)(sum n)/(1-n^(2))=

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  5. underset(n to oo)lim (n(1^(3)+2^(3)+...+n^(3))^(2))/((1^(2)+2^(2)+...+...

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  6. underset(n to oo)lim (1+3+5+....+(2n-1))/(2+4+6+..2n)

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  7. underset(n to oo)lim (1+3+3^(2)+...3^(n))/(1+2+2^(2)+...+2^(n))=

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  8. Lt(x to oo) (1+(1)/(3)+(1)/(9)+.....+(1)/(3^(n)))/(1+(1)/(5)+(1)/(25)+...

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  9. underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

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  10. Lt(x to oo)[(1)/(n^(2)-1)+(2)/(n^(2)-1)+....+(n)/(n^(2)-1)]=

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  11. If 0lt x lt y then Lt(x to oo) (y^(n)+x^(n))^(1//n)=

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  12. Lt(x to oo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  13. If 0 lt a< b then Lt(x to oo) (a^(n+3)+b^(n+3))/(a^(n)+b^(n))=

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  14. underset(n to oo)lim (1.1!+2.2!+3.3!+...+n.n!)/((n+1)!)=

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  15. Lt(x to oo) ((1)/(a(a+d))+(1)/((a+d)(a+2d))+.....+(1)/([a+(n-1)d][a+n...

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  16. Lt(n to oo) ((1)/(1.5)+(1)/(5.9)+....+(1)/((4n-3)(4n+1)))=

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  17. f(x)={(x)/(1+x)+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+....n terms} and ...

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  18. If |x| lt 1" thn "underset(n to oo)"Lt "(1+x)(1+x^(2))(1+x^(4))....(1+...

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  19. If [.] denote the greatest ineger function then Lt(x to oo) ([x]+[2x]+...

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  20. If [.] denotes the greatest integer functon, then Lt(n to oo)([1^(3)x]...

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