COMEDK · Maths · 16. Limits
The value of \(\lim\limits_{x \to 3}\left[\dfrac{1}{x-3} + \dfrac{9x}{27-x^3}\right]\) is:
- A \(1\)
- B \(2\)
- C \(\dfrac{1}{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
The given limit is \(\lim\limits_{x \to 3}\left[\dfrac{1}{x-3} + \dfrac{9x}{27-x^3}\right]\) Using the identity \(a^3 - b^3 = (a-b)(a^2+ab+b^2)\), we can write \(27 - x^3 = -(x^3 - 27) = -(x-3)(x^2+3x+9)\) Substituting this into the limit expression:…
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