InterviewSolution
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InterviewSolution
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Evaluate: `lim_(xrarr0) ((3+x)^(1//2)-(3-x)^(1//2))/(x)` |
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Answer» ` underset(xrarr0)"lim"((3+x)^(1//2)-(3-x)^(1//2))/(x)` `=underset(xrarr0)"lim"(sqrt(3+x)^(1//2)-(3-x)^(1//2))/(x)xx(sqrt(3+x)+sqrt(3-x))/(sqrt(3+x)+sqrt(3-x))` `=underset(xrarr0)"lim"(2x)/(x(sqrt(3+x)+sqrt(3-x)))` `underset(xrarr0)"lim"(2x)/(sqrt(3+x)+sqrt(3-x))` `=(2)/(sqrt(3)+sqrt(3))=(1)/sqrt(3)` |
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