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The value of lim_(nto oo){3sqrt(n^2-n^3)+n}, is |
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Answer» `(1)/(3)` `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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