Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxi)

Provide solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxi)

Answers (1)

best_answer

Answer: 3.00926

Hint: Here we use below formula,

        \Delta y=f(x+\Delta x)-f(x)

Given:(82)^{\frac{1}{4}}

Solution: x=81

\Delta x=1

on differentiating  f(x) with respect to  x

\frac{d f}{d x}=\frac{d}{d x}\left(x \frac{1}{4}\right)

we know  \frac{d}{d x}\left(x^{3}\right)=n x^{n-1}

\begin{aligned} &\frac{d f}{d x}=\frac{1}{4} x^{\frac{1}{4}-1} \\\\ &\frac{d f}{d x}=\frac{1}{4} x^{\frac{3}{4}}=\frac{1}{4 x^{\frac{3}{4}}} \end{aligned}

\begin{aligned} &\Rightarrow \text { when } x=81 \text { we have } \frac{d f}{d x}=\frac{1}{4(81)^{\frac{3}{4}}} \\\\ &\Rightarrow \frac{d f}{d x}=\frac{1}{4(34)^{\frac{3}{4}}}=\frac{1}{4\left(3^{3}\right)}=\frac{1}{4 \times 27}=\frac{1}{108}=0.00926 \end{aligned}

\begin{aligned} &\Rightarrow \Delta y=\left(\frac{d y}{d x}\right) \Delta x \\\\ &\Delta f=0.00926 \\\\ &\Rightarrow \text { now, } f(82)=f(81)+\Delta f \end{aligned}

\begin{aligned} &f(82)=3+0.00926 \\\\ &f(82)=3.00926 \end{aligned}

 

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
anam-khan

CBSE compartment admit card 2024 out at cbse.gov.in; exams from July 15
anam-khan

Reports saying CBSE cannot conduct board exams twice a year currently ‘totally incorrect’; board denies claims

Latest Question