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If x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h ...

If `x_1=3a n dx_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xvecoo)x_n` is `-1` (b) `2` (c) `sqrt(5)` (d) 3

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 x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xvecoo)xn is -1 ...

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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),a n dh(x)=-(2(2x+1))/(x^2+x-12),t h e...

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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)i s (a)1/(...

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  9. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  10. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  11. about to only mathematics

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  12. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

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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. evaluate (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underse...

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

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  16. ("lim")(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n-1))i se q u a lto 0 (b) 2...

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  17. ("lim")(xvecoo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45))i se q u a lto 16 (...

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

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  19. about to only mathematics

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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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