The approximate value of $\sqrt[3]{0 \cdot 026}$ is

The approximate value of $\sqrt[3]{0 \cdot 026}$ is
  1. 0.2762
  2. 0.2963
  3. 0.2632
  4. 0.2692

Solution

Let $\mathrm{f}(x)=\sqrt[3]{x}=x^{\frac{1}{3}}$ $\therefore \quad \mathrm{f}^{\prime}(x)=\frac{1}{3} x^{-\frac{2}{3}}=\frac{1}{3 x^{\frac{2}{3}}}$
Here, $\mathrm{a}=0.027$ and $\mathrm{h}=-0.001$ $\begin{aligned} & \therefore \quad f(a)=f(0.027)=(0.027)^{\frac{1}{3}}=0.3 \text { and } \\ & \mathrm{f}^{\prime}(\mathrm{a})=\mathrm{f}^{\prime}(0.027) \\ & =\frac{1}{3(0.027)^{\frac{2}{3}}} \\ & =\frac{1}{3(0.09)}=\frac{1}{0.27} \\ & \therefore \quad \mathrm{f}(\mathrm{a}+\mathrm{h}) \approx \mathrm{f}(\mathrm{a})+\mathrm{hf}^{\prime}(\mathrm{a}) \\ & \approx 0.3-\frac{0.001}{0.27} \\ & \approx 0.3-0.0037 \\ & \approx 0.2963 \end{aligned}$

Asked in: MHT CET 2024 (02 May Shift 2)

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