Study Guide

Key Concepts — NUPOC Interview Prep

A concise equation sheet with plain-English context for every topic on the Naval Reactors study list. Use it to refresh before you start solving problems. Engineering approximations (g ≈ 10, π ≈ 3, sin θ ≈ θ) are always accepted — precision of reasoning matters more than precision of arithmetic.

37 topics across 4 sections.

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Limits of a Function

Calculus 1

Limits of a Function

$\lim_{x \to 0} \frac{\sin x}{x} = 1 \qquad \lim_{n \to \infty}\!\left(1 + \tfrac{1}{n}\right)^{n} = e$

A limit asks what value does $f(x)$ approach as $x$ approaches a target, regardless of whether $f$ is defined at that target. One-sided limits look at $x \ o a^{-}$ (from the left) or $x \ o a^{+}$ (from the right); the two-sided limit exists only when both agree. A function is continuous at $a$ when $\lim_{x \ o a} f(x) = f(a)$ . Continuity is what lets the Intermediate Value Theorem guarantee that a continuous function crossing zero must pass through zero somewhere.

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