COMEDK · Maths · 28. Indefinite Integration
Evaluate: \(\lim _{x \rightarrow 0} \dfrac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}{x}\)
- A \(\dfrac{2}{3}\)
- B \(\dfrac{1}{3}\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(\dfrac{2}{3}\)
Step-by-step Solution
Detailed explanation
Let \(f(x) = \dfrac{(1+x)^{1/3} - (1-x)^{1/3}}{x}\). Using the binomial expansion \((1+u)^n = 1 + nu + \dfrac{n(n-1)}{2!}u^2 + \dots\) for small \(u\), we have:…
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