InterviewSolution
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InterviewSolution
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Evaluate `lim_(xto0) ((a^(x)+b^(x)+c^(x))/(3))^(2//x),(a,b,cgt0)` |
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Answer» We have `underset(xto0)lim((a^(x)+b^(x)+c^(x))/(3))^(2//x)=e^(underset(xto0)lim((a^(x)+b^(x)+c^(x))/(3)-1).2/x` `=e^(2/3underset(xto0)lim((a^(x)+b^(x)+c^(x)-3)/(x))` `=e^(2/3underset(xto0)lim((a^(x)-1)/(x)+(b^(x)-1)/(x)+(c^(x)-1)/(x))` `=e^(2/3{underset(xto0)lima^(x-1)/(x)+underset(xto0)lim(b^(x)-1)/(x)+underset(xto0)lim(c^(x)-1)/(x)}}` `=e^((2//3){"In "a+"In "b+"In "c}}` `=e^((2//3)"In"(abc))` `=e^("In"(abc)^(2//3))` `=(abc)^(2//3)` |
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