1. **State the problem:** Find the limit $$\lim_{x \to \pi} 3 + \cos(x)$$. 2. **Recall the limit rule:** If a function is continuous at the point where the limit is taken, then the limit is simply the function value at that point. 3. **Check continuity:** The cosine function, $\cos(x)$, is continuous everywhere, including at $x = \pi$. 4. **Evaluate the limit by direct substitution:** $$\lim_{x \to \pi} 3 + \cos(x) = 3 + \cos(\pi)$$ 5. **Calculate $\cos(\pi)$:** $$\cos(\pi) = -1$$ 6. **Final answer:** $$3 + (-1) = 2$$ **Recommendation for a more challenging problem:** You could consider a limit involving a trigonometric expression that requires algebraic manipulation or use of trigonometric identities, for example: $$\lim_{x \to 0} \frac{1 - \cos(3x)}{x^2}$$ This requires using the identity $1 - \cos(\theta) = 2\sin^2(\frac{\theta}{2})$ and applying limit properties. This keeps the problem basic but adds a layer of challenge through algebraic manipulation and trigonometric identities.