The approximate value of $(3.978)^{\frac{3}{2}}$ is

The approximate value of $(3.978)^{\frac{3}{2}}$ is
  1. 7.934
  2. 8.934
  3. 7.022
  4. $8.866^{\circ}$

Solution

$\begin{aligned} & \text { Let } \mathrm{f}(x)=x^{\frac{3}{2}} \\ & \therefore \quad \mathrm{f}^{\prime}(x)=\frac{3}{2} x^{\frac{1}{2}} \\ & \text { Here, } \mathrm{a}=4, \mathrm{~h}=-0.022 \\ & \mathrm{f}(3.978)=(4)^{\frac{3}{2}}=-0.022 \times \frac{3}{2} \times(4)^{\frac{1}{2}} \\ &=8-0.033 \times 2 \\ &=8-0.066=7.934\end{aligned}$

Asked in: MHT CET 2024 (11 May Shift 1)

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