Limits, Continuity & Differentiability
Limit Evaluation
Grade 12
Question:
<p><strong>Problem 2(D):</strong> If $f(x) = \cos^{-1}(4x^3 - 3x)$ and $\lim_{x \to \frac{1}{2}^+} f'(x) = a$ and $\lim_{x \to \frac{1}{2}^-} f'(x) = b$, then find $a + b + 3$</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: Differentiate the inverse cosine function and evaluate the left and right limits at the boundary point.
<p>Answer: 2(D) → Q</p>
Correct Answer: Q