`lim_(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0,` is equal to
`lim_(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0,` is equal to
A. `pi`
B. `2pi`
C. `pi//2`
D. none of these
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Correct Answer - C
`underset(ntooo)limn^(2)(x^(1//n)-x^((1)/(n+1)))=underset(ntooo)limn^(2).x^((1)/(n+1))(x^((1)/(n)-(1)/(n+1))-1)`
`=underset(ntooo)limx^((1)/(n+1))(x^((1)/(n(n+1)))-1)n^(2)`
`=underset(ntooo)limx^((1)/(n+1)).(x^((1)/(n(n+1)))-1)/((1)/(n(n+1))).(n^(2))/(n(n+1))`
`=1.log_(e)x.1=log_(e)x`
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