Lesson 19 of 48
Limits
What a value approaches, including where it never arrives.
The limit is the crowbar that pries calculus open: it lets you talk about an instant without dividing by zero. Everything in phase 3 is a limit taken carefully.
Do this
Evaluate a limit that direct substitution cannot reach, both numerically from each side and algebraically, and show the two agree. Then construct a function whose limit exists where its value does not.
The question that unlocks the next lesson
A limit at x = 2 exists and equals 5. What does that guarantee about f(2)?
- Af(2) = 5
- BNothing — f(2) may be a different value, or undefined
- Cf(2) is undefined
- Df is continuous at 2