Limits, Continuity & Differentiability
Limit Evaluation
Grade 12
Question:
<p><strong>Problem 2(A):</strong> If $f(x) = \sin^{-1} x$ and $\lim_{x \to \frac{1}{2}^+} f(3x - 4x^3) = a - 3 \lim_{x \to \frac{1}{2}^+} f(x)$, then find $[a]$ 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: Recognize the triple angle formula for inverse sine and substitute appropriate values.
<p>Answer: 2(A) → Q</p>
Correct Answer: Q