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lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt...

`lim_(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)]` is equal to

A

1

B

0

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xtooo)lim[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)]=underset(xtooo)lim(x+sqrt(x+sqrt(x))-x)/(sqrt(x+sqrt(x+sqrt(x)))+sqrt(x))`
(Rationalizing)
`underset(xtooo)lim(sqrt(1+x^(-1//2)))/(sqrt(1+sqrt(x^(-1)+x^(-3//2)))+1)=1/2`
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

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  2. lim(xtooo) ((2x+1)^(40)(4x+1)^(5))/((2x+3)^(45)) is equal to

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  3. lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

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  4. lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

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  5. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

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  6. lim(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2...

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  7. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

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  8. lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

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  9. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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  10. f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x))). Then lim(x to oo) f(x) ...

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  11. The value of lim(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n+1)-(n)/(1-2n).(...

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  12. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  13. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  14. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  15. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  16. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  17. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  18. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  19. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  20. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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