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lim(x->oo)[sqrt(x+sqrt(x+sqrt(x)))-sqrt(...

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

(a)0

(b) `1/2`

(c) log 2

(d) `e^4`

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 PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) ...

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  2. lim(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 ...

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  3. lim(x->oo)[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to (a)0 (...

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

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

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  6. lim(x->oo)(2sqrt(x)+3x3+4x4++n x n)/(sqrt((2x-3))+(2x-3)3++(2x-3)n) ...

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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(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x ...

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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)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

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  11. The value of lim(n->oo)[(2n)/(2n^2-1)cos((n+1)/(2n-1))-n/(1-2n)dot(n(-...

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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")(xvecoo)(x^2tan1/x)/(sqrt(8x^2+7x+1))i se q u a lto: -1/(2sqrt...

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  15. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

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  16. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  17. lim(x->1)(1-x^2)/(sin2pix) is equal to (a)1/(2pi) (b) -1/pi (...

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  18. ("lim")(xto0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equals to (a)1 (b) 0 ...

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  19. lim(y->0)((x+y)sec(x+y)-xsecx)/y is equal to (a) secx(xtanx+1) (b) x...

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

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