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CBSE Class 12-science Answered

Find left parenthesis 27.7 right parenthesis to the power of bevelled 1 third end exponent  using differentials.
Asked by Topperlearning User | 05 Aug, 2014, 02:07: PM
answered-by-expert Expert Answer

We start answering this question by defining a relationship between dependent variable 'y' independent variable 'x', say

(Here the power of 'x' will be the same as that given in the question).

 We choose 'x' in such a way that its cube root can be calculated easily.

 For example:  We can take 'x' as 27 as its cube root is 3.

Now, in this question we can take x as 27 and increment straight x as 0.7 so that  is 27+0.7=27.7

This means,

increment straight y equals left parenthesis straight x plus increment straight x right parenthesis to the power of bevelled 1 third end exponent minus straight x to the power of bevelled 1 third end exponent space space space space space space equals left parenthesis 27.7 right parenthesis to the power of bevelled 1 third end exponent minus left parenthesis 27 right parenthesis to the power of bevelled 1 third end exponent space space space space space space equals left parenthesis 27.7 right parenthesis to the power of bevelled 1 third end exponent minus space 3 left parenthesis 27.7 right parenthesis to the power of bevelled 1 third end exponent equals increment straight y plus 3 Now comma dy equals open parentheses dy over dx close parentheses increment straight x Differentiating space straight y space with space respect space to space straight x space in space the space equation space straight y equals straight x to the power of bevelled 1 third end exponent rightwards double arrow dy over dx equals 1 third straight x to the power of minus bevelled 2 over 3 end exponent rightwards double arrow dy equals open parentheses fraction numerator 1 over denominator 3 left parenthesis 27 right parenthesis to the power of begin display style bevelled 2 over 3 end style end exponent end fraction close parentheses cross times 0.7 rightwards double arrow dy equals 0.025

Therefore the approximate value of left parenthesis 27.7 right parenthesis to the power of bevelled 1 third end exponent is

3 plus increment y equals 3 plus 0.025 equals 3.025

Answered by | 05 Aug, 2014, 04:07: PM

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