DWG NO. 10 — Unit 10 of 10
5 online lessons · 1 in-person Review & Practice Day
Every function in Units 1–9 was something you could evaluate directly — plug in x, get f(x) out. This unit asks a subtler question: what does f(x) do as x gets close to some value, whether or not f is even defined right there? That question is the limit, and it's the one idea that finally lets you talk precisely about instantaneous change — a slope at a single point, a speed at a single instant — instead of just the average rate over some stretch.
The unit starts by building the idea intuitively from tables and graphs, then makes it computable with algebraic techniques you already know: factoring, rationalizing, and the end-behavior reasoning from Unit 2's rational functions. From there it defines continuity precisely, and closes with the derivative — the limit that turns a secant line into a tangent line, and an average rate of change into an instantaneous one. This is the bridge to Calculus.
The Intuitive Idea of a Limit
What li\(m_{x→a}\) f(x) means, estimating it from tables and graphs, and one-sided limits.
→Evaluating Limits Algebraically
Direct substitution, the limit laws, and resolving 0/0 forms by factoring or rationalizing.
→Limits at Infinity and Asymptotic Behavior
Evaluating limits as x → ±∞ and connecting them to horizontal asymptotes.
→Continuity
The three-part definition of continuity at a point, and classifying removable, jump, and infinite discontinuities.
→Introduction to the Derivative as a Rate of Change
From average rate of change (a secant slope) to instantaneous rate of change (a tangent slope) using the limit definition of the derivative.
→Review & Practice Day 10 + Cumulative Final Review — bring your questions from lessons 10.1–10.5. You'll work practice problems, get feedback, review the full course, and take the Unit 10 test and cumulative final.