Limits, Continuity & Differentiability
Limit Evaluation
Grade 12
Question:
<p><strong>Problem 2(B):</strong> If $f(x) = \tan^{-1} g(x)$ where $g(x) = \frac{3x - x^3}{1 - 3x^2}$, then find $\lim_{h \to 0} \frac{f\left(\frac{1}{6} + 6h\right) - f\left(\frac{1}{6}\right)}{6h}$</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 tangent and compute the derivative at the given point.
<p>Answer: 2(B) → P</p>
Correct Answer: P