InterviewSolution
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InterviewSolution
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Evaluate `lim_(xto0) ((x+2)^(1//3)-2^(1//3))/(x)` |
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Answer» Given, `underset(xto0)"lim"((x+2)^(1//3)-2^(1//3))/(x) = underset(xto0)"lim"((x+2)^(1//3)-2^(1//3))/((x+2)-2)` `=1/3 xx 2^(1//3-1)` `=1/3 xx (2)^(-2//3)` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a) = na^(n-1)]` `=1/(3(2)^(2//3))` `[therefore x to 0 rArr x+2 to 2]` |
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