RD Sharma Solutions Class 12 Mathematics Chapter 13 FBQ

# RD Sharma Solutions Class 12 Mathematics Chapter 13 FBQ

Edited By Satyajeet Kumar | Updated on Jan 27, 2022 10:01 AM IST

One of the top-rated NCERT solutions today is the RD Sharma class 12th exercise FBQ book. RD Sharma solutions have been a trusted name in the education industry for a very long time. In India, hundreds of school students have chosen this NCERT solution for their exam preparations and have greatly benefited from it. The RD Sharma class 12 chapter 13 exercise FBQ is one such NCERT solution from RD Sharma which requires special mention.

The RD Sharma class 12th exercise FBQ solution includes the 13th chapter of the NCERT maths book which is Differentials, Errors, and Approximations. The various topics present in this chapter are types of errors like Absolute, relative, and percentage error. There are a couple of important questions given in this part that must be concentrated on.

Also Read - RD Sharma Solutions For Class 9 to 12 Maths

## Differentials, Errors and Approximations Excercise: FBQ

Differentials Errors and Approximations exercise fill in the blanks question 1

Answer: $\Delta y=-0.27$
Hint: Here we use this below formula,
$F(a+h)=F(a)+h F^{\prime}(a)$
Given: $y=x^{3}+5$
Solution:
Here $y=x^{3}+5$ ………………. eqn 1
As we know that,
$\frac{\Delta y}{\Delta x}=\frac{d y}{d x}$
$\Delta y$ denotes the changes in $y$
$\Delta x$ denotes the changes in $x$
$\Rightarrow \Delta y=\frac{d y}{d x} \times \Delta x$ ……………..eqn 2
Differentiating the given equation (1) with respect to $x$
We get,
$\Rightarrow \frac{d y}{d x}=3 x^{2}$
Put this value in equation (2)
$\Rightarrow \Delta y=3 x^{2} \times \Delta x$ ………..eqn 3
Since it is given that…….
$\Delta x=2.99-3$ ($x$ is changing from 3 to 2.99)
$\therefore \Delta x=-0.01$
Put this value in equation (3)
\begin{aligned} &\Rightarrow \Delta y=3 x^{2} \times-0.01 \\\\ &\Rightarrow \Delta y=3(3)^{2} \times-0.01 \\\\ &\Rightarrow \Delta y=27 \times-0.01 \\\\ &\Rightarrow \Delta y=-0.27 \end{aligned}
Note : Derivate of a function tells us the value of change in function by changing the value of an independent variable .So,$\frac{dy}{dx}$ tells us about the changing in value of $y$ with respect to change in $x$.

Differentials Errors and Approximations exercise fill in the blanks question 2

Answer:$0.06 x^{3} m^{3}$
Hint: Here we use the formula of volume of cube,
$V=x^{3}$
Given: Side of the cube $=x \; meter$
Also,increase in side $=2%$ of side
Solution:
Increase in side $=2%$ of side $=0.02x$
Hence, $\Delta x=0.02 x$
And volume of the cube, $V=x^{3} m^{3}$
We need to find approximate change in volume of the cube
Now, $\Delta V=\frac{d V}{d x} \Delta x$
\begin{aligned} &=\left(\frac{d V}{d x}\right) \times \Delta x \\\\ &\Rightarrow 3 x^{2} \times 0.02 x \end{aligned} [because 2% of $0.02x$ is=$0.02x$]
$=0.06 x^{3}$
Hence, the approximate change in the volume of the cube is $0.06 x^{3} m^{3}$

The RD Sharma class 12th exercise FBQ can be a unique guidebook for students who are in class 12. To know about the book in detail take a look at these top features of the class 12 RD Sharma chapter 13 exercise FBQ solution:-

• RD Sharma class 12th exercise FBQ contains questions from the entire chapter of Differentials, Errors, and Approximations. Students can easily use this book to test their knowledge about the chapter.

• The RD Sharma class 12 solutions Differentials, Errors, and Approximations ex FBQ is updated regularly to include all questions in the NCERT textbooks. Hence, students will always be up-to-date with their syllabus.

• School teachers like to give questions from the RD Sharma class 12 solutions chapter 13 ex FBQ book as homework assignment. Students can use the solutions in this book to answer complicated questions and check their performance.

• Highly skilled professionals with immense knowledge in maths have joined hands to create the answers in the book. Therefore, the answers will always be accurate and of high-quality.

• Students can find common questions in their board exams if they practice the class 12 RD Sharma chapter 13 exercise FBQ solution thoroughly.

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