JEE Mains · Maths · STD 11 - 12. limits
Let \(f(x) = \lim_{y \to 0} \dfrac{(1 - \cos(xy)) \tan(xy)}{y^3}\). Then the number of solutions of the equation \(f(x) = \sin x\), \(x \in \mathbf{R}\) is :
- A \(0\)
- B \(2\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
The given function is \(f(x) = \lim_{y \to 0} \dfrac{(1 - \cos(xy)) \tan(xy)}{y^3}\). Multiplying and dividing by \(x^3\), we get: \(f(x) = \lim_{y \to 0} \dfrac{1 - \cos(xy)}{(xy)^2} \cdot \dfrac{\tan(xy)}{xy} \cdot x^3\) Using the standard limits…
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