InterviewSolution
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InterviewSolution
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Evaluate `lim_(hto0)(sqrt(x+h)-sqrt(x))/(h)` |
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Answer» Given, `underset(hto0)"lim"(sqrt(x+h)-sqrt(x))/(h) = underset(hto0)"lim"((x+h)^(1//2)-(x)^(1//2))/(x+h-x)` `=underset(hto0)"lim"((x+h)^(1//2)-(x)^(1//2))/((x+h)-x)` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a) = na^(n-1)]` `=1/2x^(1/2-1) = 1/2x^(-1//2)` `[therefore h-0 rArr x+h to x]` `=1/(2sqrt(x))` |
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