The approximate value of $(3 \cdot 978)^{3 / 2}$ is

Question

Aicharya · Accepted Answer

$\begin{array}{ll} & 	ext { Let } \mathrm{f}(x)=x^{\frac{3}{2}} \ 	herefore \quad & \mathrm{f}^{\prime}(x)=\frac{3}{2} x^{\frac{1}{2}} \end{array}$ Here, $\mathrm{a}=4$ and $\mathrm{h}=-0.022$. $\begin{aligned} & \ & f(a)=f(4)=4^{\frac{3}{2}}=8 \ & f^{\prime}(a)=f^{\prime}(4)=\frac{3}{2}(4)^{\frac{1}{2}}=3 \ & 	herefore \quad f(a+h) \approx f(a)+h f^{\prime}(a) \ & \approx 8+(-0.022)(3) \ & \approx 8-0.066 \ & \approx 7.934\end{aligned}$

The approximate value of $(3 \cdot 978)^{3 / 2}$ is

Solution