`lim_(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)]` is equal to
`lim_(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)]` is equal to
A. 1
B. 0
C. 2
D. none of these
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Correct Answer - 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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