Limits, Continuity & Differentiability
Limits of trigonometric expressions
Grade 12
Question:
<p>The value of $\lim_{n \to \infty} \cos^2\left(\pi\left(3n^3 + n^2 + 2n\right)\right)$ (where $n \in \mathbb{N}$):</p>
<p>(a) $\frac{1}{3}$</p>
<p>(b) $\frac{1}{2}$</p>
<p>(c) $\frac{1}{4}$</p>
<p>(d) $\frac{1}{9}$</p>
Step-by-Step Solution
Key Concept: Evaluate the periodic behavior of cosine at the limit and extract the fractional part of the argument.
<p>The answer is (c).</p>
Correct Answer: C