1.

The value of lim_(nto oo){3sqrt(n^2-n^3)+n}, is

Answer»

`(1)/(3)`
`(-1)/(3)`
`(2)/(3)`
`(-2)/(3)`

SOLUTION :We have,
`lim_(xto oo) {3sqrt(N^2-n^3)+n}`
` rArr l=lim_(NTO oo) {n 3sqrt((1)/(n)-1)+n}=lim_(n to oo) n{((1)/(n)-1)^(1//3)+1^(1//3)}`
` because a+b=(a^3+b^3)/(a^2-ab+b^2)`
`therefore l=lim_(nto oo) n[(((1)/(n-1)+1))/(((1)/(n)-1)^(2//3)-((1)/n-1)^(1//3)+1)]`
`therefore l=lim_(nto oo) n[(1)/(((1)/(n)-1)^(2//3)-((1)/n-1)^(1//3)+1)]=(1)/(3)` .


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