- Sign up for appointments to grade the problem set!
- ε = “epsilon”
- δ = “delta”
- Section 2.3
- Significance of ε and δ?
- Role of absolute values?
- Y Distance from L = f(x) - L
- “within ε” could be -ε < f(x) - L < ε
- or equivalently | f(x) - L | < ε
- Example 1’s “2x - 8”?
- Comes from function definition (y = 2x - 1) and proposed limit (7)
- “Didn’t know what I didn’t know”—what to do when this happens?
- Notice where it happened, so you can at least identify the point where you got lost
- Check other sources (e.g., Math Learning Center, Khan Academy, Patrick JMT on YouTube, etc.)
- Don’t panic
- Examples
- Suppose you believe that limx→14x = 4, and I
challenge you with ε = 0.5. Find a δ that supports your belief
- | 4x - 4| < 0.5
- - 0.5 < 4x - 4 < 0.5
- 3.5 < 4x < 4.5
- 7/8 < x < 9/8
- -1/8 < x - 1 < 1/8
- | x - 1 | < 1/8 = δ
- Suppose you believe that limx→14x = 4, and I
challenge you with ε = 0.5. Find a δ that supports your belief
- Finish formal definition examples