OAT Quantitative Reasoning: Calculus Mastery Hub: The Indust

Considering the foundational principles of limits as presented in "The Complete OAT Calculus Limits & Continuity Course 2026," which of the following statements most accurately reflects the epsilon-delta definition of a limit, specifically $\lim_{x \to c} f(x) = L$?

In the context of continuity as explored in the OAT Calculus Mastery Hub, a function $f(x)$ is continuous at a point $c$ if and only if $\lim_{x \to c} f(x) = f(c)$. If a function is not continuous at $c$, it possesses a discontinuity. Which type of discontinuity is characterized by a finite jump between the left-hand limit and the right-hand limit at that point?

The OAT Calculus Mastery Hub emphasizes the practical application of limit theorems. Consider the function $g(x) = \frac{\sin(3x)}{x}$ as $x \to 0$. To evaluate $\lim_{x \to 0} g(x)$ using fundamental limit properties, what key manipulation is typically employed, and what is the resulting limit?