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Find underset(n to oo)lim x(n) if (a) ...

Find `underset(n to oo)lim x_(n)` if
(a) `x_(n=sqrt(2n+3)-sqrt(n-1)`
(b) `x_(n)=sqrt(n^(2)+n+1)-sqrt(n^(2)-n+1)`,
(c) `x_(n)=n^(2) (n-sqrt(n^(2)+1))`
(d) `x_(n)=root3(n^(2)-n^(3))+pi`
(e) `x_(n)=(sqrt(n^(2)+1)+sqrtn)/(root5(n^(3)+n-sqrtn)`
(f) `x_(n)=root(n+1)^(2)-root3(n-1)^(2)`,
(g) `x_(n)=(1-2+3-4+5-6+...-2n)/(sqrt(n^(2)+!)+sqrt(4n^(2)-1))`
(g) `x_(n)=1/(1.2)+1/(2.3)+(1)/(3.4)+.....+(1)/(n(n+10)`

Text Solution

Verified by Experts

The correct Answer is:
(b) 1; (f) 0
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