Topic 1 of 6
Limits & Continuity
How functions behave near a point, when substitution is legal, and what continuity actually promises.
01Calculus · Direct answerWhy is the limit of sin x over x equal to 1?A foundational limit whose real proof comes from geometry, not from plugging in zero and hoping.02Calculus · Method guideHow to evaluate an indeterminate limitA decision process for 0/0 and ∞/∞ that starts with algebra before reaching for a theorem.03Calculus · Concept explainerWhat continuity at a point really requiresThree conditions, one precise promise: nearby inputs produce nearby outputs without a break at the point.04Calculus · Method guideHow and when to use the Squeeze TheoremTrap a difficult function between two easier functions that are forced to meet at the same limit.05Calculus · Concept explainerInfinite limits and vertical asymptotesInfinity describes unbounded behavior, not a number a function eventually reaches.