WBJEE · Maths · Functions
In the interval \((-2 \pi, 0)\), the function \(f(x)=\sin \left(\frac{1}{x^3}\right)\)
- A never changes sign
- B changes sign only once
- C changes sign more than once but finitely many times
- D changes sign infinitely many times
Answer & Solution
Correct Answer
(D) changes sign infinitely many times
Step-by-step Solution
Detailed explanation
Hint : \(x \in(-2 \pi, 0), f(x)=\sin \left(\frac{1}{x^3}\right)\) \(\begin{aligned} & \because-2 \pi < x < 0 \\ & \Rightarrow-8 \pi^3 < x^3 < 0 \\ & \Rightarrow-\infty < \frac{1}{x^3} < -\frac{1}{8 \pi^3} \end{aligned}\) Hence, \(\sin \left(\frac{1}{x^3}\right)\) will take all…
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