COMEDK · Maths · 27. Application of Derivatives
The approximate value of \((0.026)^{\overline{3}}\) is
- A \(\frac{7}{27}\)
- B \(\frac{8}{27}\)
- C \(\frac{5}{27}\)
- D \(\frac{4}{27}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{27}\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=x^{\frac{1}{3}}\) and \(x=0.027\) \(\Delta x=-0.001\) Now use, \(f(x+\Delta x)=f(x)+\Delta x f^{\prime}(x)\) \(\therefore f^{\prime}(x)=\frac{1}{3(x)^{\frac{2}{3}}}\) Now, \(f(0.027) \simeq f(0.027)-(0.001) \times \frac{1}{3(0.027)^{\frac{2}{3}}}\)…
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