CBSE Class 12-science Answered
Using differentials find the approx value
(27)1/3
Asked by haroonrashidgkp | 08 Sep, 2018, 16:18: PM
(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](https://images.topperlearning.com/topper/tinymce/cache/e27d629d3d5802e2c596dff3d7f7079d.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/e27d629d3d5802e2c596dff3d7f7079d.png)
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](https://images.topperlearning.com/topper/tinymce/cache/d949cad51e9db73394d799fc6ba99eae.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/d949cad51e9db73394d799fc6ba99eae.png)
Put it in the formula
f(x + h) ≈ f(x) + h f'(x)
you will get the answer 5.0266
Answered by Sneha shidid | 13 Sep, 2018, 18:31: PM
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