Limits, Continuity & Differentiability
Limit Evaluation
Grade 12
Question:
<p><strong>Problem 2(C):</strong> If $\cos^{-1}(4x^3 - 3x) = a + b\cos^{-1}x$ for $-1 < x < \frac{1}{2}$, then find $[a + b + 2]$ where $[\cdot]$ is the greatest integer function.</p>
<p>(P) 2</p>
<p>(Q) 3</p>
<p>(R) 4</p>
<p>(S) -2</p>
<p>(T) Non-existent</p>
Step-by-Step Solution
Key Concept: Use the triple angle formula for inverse cosine: $\cos^{-1}(4x^3 - 3x) = 3\cos^{-1}x$.
<p>Answer: 2(C) → S</p>
Correct Answer: S