#### Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise fill in the blanks question 1 maths textbook solution

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 $x$.