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CBSE Class 12-science Answered

Using differentials find the approx value (27)1/3
Asked by haroonrashidgkp | 08 Sep, 2018, 04:18: PM
Expert Answer
(27)1/3 = 3 obviously.
 
The question might be (127)1/3 
f(x) = x1/3 
a = 125 and h = 2
f(125) = 5 and f'(x) = begin mathsize 16px style 1 third straight x to the power of 1 third minus 1 end exponent equals fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction straight x to the power of fraction numerator negative 2 over denominator 3 end fraction end exponent equals fraction numerator begin display style 1 end style over denominator begin display style 3 straight x to the power of 2 over 3 end exponent end style end fraction end style
f'(125) = begin mathsize 16px style fraction numerator 1 over denominator 3 cross times open parentheses 125 close parentheses to the power of begin display style 2 over 3 end style end exponent end fraction equals 1 over 75 end style
Put it in the formula 
f(x + h) ≈ f(x) + h f'(x)
you will get the answer 5.0266
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