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

Answers (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


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.


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