Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. Evaluate $\lim_{\theta \to 0} \frac{\sin(4\theta)}{3\theta}$ without using L'Hopital's Rule.

Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. Use the provided table of values to estimate $\lim_{x \to 1} f(x)$. Assume $f$ is smooth. Values near $x=1$ approach $2.71$. Provide a concise written explanation.

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Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. Evaluate $\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$ and identify the type of discontinuity.

Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. Given $f(x) = \frac{|x-3|}{x-3}$, compute the one-sided limits as $x$ approaches 3 from the left and right. Provide a concise written explanation.

Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. Suppose $g(x)$ is continuous on [1, 5] with g(1) = -2 and g(5) = 4. Use the IVT to justify if g(c) = 0 for some $c \in (1, 5)$.

Exam-style application: In a limits and continuity setting, use one-sided limits, removable discontinuities, vertical asymptotes, continuity conditions, IVT, and squeeze theorem. If $-x^2 + 3 \le h(x) \le x^2 + 3$ for all $x$, evaluate $\lim_{x \to 0} h(x)$ using the Squeeze Theorem. Provide a concise written explanation.