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If x(1)=3 and x(n+1)=sqrt(2+x(n))" ",nge...

If `x_(1)=3` and `x_(n+1)=sqrt(2+x_(n))" ",nge1,` then `lim_(ntooo) x_(n)`is

A

0

B

`(1)/(2)`

C

log2

D

`e^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
`x_(n+1)=sqrt(2+x_(n))`
or `underset(ntooo)limx_(n+1)=sqrt(2+underset(ntooo)limx_(n))`
or `t=sqrt(2+t)" "(becauseunderset(xtooo)limx_(n+1)=underset(xtooo)limx_(n)=t)`
or `t^(2)-t-2=0`
or`(t-2)(t+1)=0`
or `t=2" "(becausex_(n)gt0AAn,tgt0)`
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CENGAGE-LIMITS-Exercise (Single)
  1. If lim(xtoa) {(f(x))/(g(x))} exists, then

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  2. ("lim")(xvec1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional ...

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  3. If x(1)=3 and x(n+1)=sqrt(2+x(n))" ",nge1, then lim(ntooo) x(n)is

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  4. lim(xto0^(+)) (sum(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where nin...

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  5. lim(xtooo) (sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1)is equal to

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  6. If f(x)=(2)/(x-3),g(x)=(x-3)/(x+4)," and "h(x)=-(2(2x+1))/(x^(2)+x-12)...

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  7. The value of lim(xto pi) (1+cos^(3)x)/(sin^(2)x)" is "

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  8. The value of lim(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

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  9. The value of lim(xto2) (2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))" is "

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  10. The value of lim(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2...

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  11. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

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  12. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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  13. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

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  14. Among (i) lim(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim(xtooo) sec^(-...

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  15. lim(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

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  16. lim(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

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

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

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

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

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