Limits, Continuity & Differentiability
Trigonometric Limits
Grade 12
Question:
<p>Find the value of \(\lim_{x \to 0} \frac{(1 - \cos 2x)(3 + \cos x)}{x \tan 4x}\)</p>
<p>(a) \(-\frac{1}{4}\)</p>
<p>(b) \(\frac{1}{2}\)</p>
<p>(c) \(1\)</p>
<p>(d) \(2\)</p>
Step-by-Step Solution
Key Concept: Apply double angle formulas and use standard limit formulas to evaluate the expression
<p>Use the identities \(1 - \cos 2x = 2\sin^2 x\) and standard limits \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) and \(\lim_{x \to 0} \frac{\tan x}{x} = 1\).</p>
Correct Answer: A