Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
0 votes

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(vii)\;(26)^{\Large\frac{1}{3}}$

This is seventh part of multipart q1

Can you answer this question?

1 Answer

0 votes
  • Let $y=f(x)$
  • $\Delta x$ denote a small increment in $x$
  • $\Delta y=f(x+\Delta x)-f(x)$
  • $dy=\big(\large\frac{dy}{dx}\big)\Delta x$
Step 1:
Let $y=x^{\Large\frac{1}{3}}$
Also let $x=27$
$\Delta x=-1$
So that $x+\Delta x=26$
$\Delta y=(x+\Delta x)^{\Large\frac{1}{3}}-x^{\Large\frac{1}{3}}$
$(26)^{\Large\frac{1}{3}}=3+\Delta y$
Step 2:
Now $\Delta y$ is approximately equal to $dy$
$dy=\big(\large\frac{dy}{dx}\big)$$\Delta x$
$\quad=\large\frac{1}{3x^{\Large\frac{2}{3}}}$$\Delta x$
$\quad=\large\frac{1}{3(27)^{\Large\frac{2}{3}}}$$\Delta x$
$\quad=\large\frac{-1}{3\times 9}$
Step 3:
Approximate value of $\Delta y=dy=-0.037037$
Hence from (1) we get,
answered Aug 5, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App