Limits, Continuity & Differentiability
L'Hôpital's Rule
Grade 12
Question:
<p><span>\(\lim_{x \to 0} \frac{f(x) \cdot g(x)}{x(1-g(x))}\)</span> will be</p>
<p>(A) 0</p>
<p>(B) -1</p>
<p>(C) 1</p>
<p>(D) 2</p>
Step-by-Step Solution
Key Concept: Apply L'Hôpital's rule or use the functional equation to evaluate the indeterminate form.
<p>Using L'Hôpital's rule or direct substitution with the given conditions <span>$f(0) \neq 0$</span> and the relationship <span>$f^2(\frac{x}{2}) = f(x)$</span>, we can evaluate this limit to get 1.</p>
Correct Answer: C