1. 14.3: One-Sided Limits and Continuity

2. 𝑥→ 𝑐 + Lim 𝑓 𝑥 =𝑁 𝑥→ 𝑐 − Lim 𝑓 𝑥 =𝑁
A one-sided limit is just what it sounds like: taking the limit, but only considering the values to the left or the right of that point.
A right limit is the limit as you approach a point from values greater than it. Denoted as
A left limit is the limit as you approach a point from values less than it. Denoted as
𝑥→ 𝑐 + Lim 𝑓 𝑥 =𝑁
𝑥→ 𝑐 − Lim 𝑓 𝑥 =𝑁

3. A function is continuous at a point if
The function is defined at that point
The right limit exists and is equal to the function at that point
The left limit exists and is equal to the function at that point

7. Find the limit using a table
𝑥→ 0 + Lim sin⁡(8𝑥) 𝑥

8. Find the limit using a table
𝑥→ 0 − Lim sin⁡(8𝑥) 𝑥

9. 𝑥→ 0 + Lim 𝑔(𝑥)
𝑥→ 2 + Lim 𝑔(𝑥)
𝑥→ 2 − Lim 𝑔(𝑥)

10. 𝑥→ 3 + Lim 𝑓(𝑥)
𝑥→ 3 − Lim 𝑓(𝑥)
𝑥→3 Lim 𝑓(𝑥)

11. Identify any points where the limit does not exist

12. Identfiy any points where the function is NOT continuous

13. 𝑥→10+ Lim 𝑓(𝑥)