Matrices & Determinants
Determinant Limits
Grade 12
Question:
<p>Let <span>\(f(x) = \begin{vmatrix} \sec x & x^2 & x \\ 2\sin x & x^3 & 4 \\ \tan 3x & x & x \end{vmatrix}\)</span>, then <span>\(\lim_{x \to 0} \frac{f(x)}{x^2}\)</span> is equal to</p>
<p>(a) 0</p>
<p>(b) -1</p>
<p>(c) 2</p>
<p>(d) 3</p>
Step-by-Step Solution
Key Concept: Expand the determinant and use Taylor series for trigonometric functions near x=0 to evaluate the limit.
<p>Evaluate the determinant and apply limit as x→0 using L'Hôpital's rule or Taylor expansions.</p>
Correct Answer: B