InterviewSolution
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InterviewSolution
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The value of `lim_(xrarr0) {(a^x+b^x+c^x)/(3)}^(1//x)`, isA. abcB. `(abc)^1//3`C. `(1)/(3)abc `D. none of these |
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Answer» Correct Answer - B `lim_(xto0) {(a^x+b^x+c^x)/(3)}^(1/x)` `lim_(xto0) {1+(a^x+b^x+c^x-3)/(3)}^(1/x)` `lim_(xto0) {1+((a^x-1)+(b^x-1)+(c^x-1))/(3)}^(1/x)` `e^(lim_(xto0) (a^x-1)/(3x)+(b^x-1)/(3x)+(c^x-1)/(3x)` `=e^((1)/(3){lim_(xto0) (a^x-1)/(3x)+lim_(xto0)(b^x-1)/(3x)+lim_(xto0)(c^x-1)/(3x)}` `=e^((1)/(3){log a+logb + log c}) =e^(log(abc) ^(1//3))=(abc) ^(1//3)`. |
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