Limits describe the y-value a graph approaches as x approaches a specific value. For a limit to exist, the graph must approach the same y-value from both sides. The squeeze theorem states that if f(x) is squeezed between g(x) and h(x) near a value except at a, and the limits of g(x) and h(x) exist and are equal, then the limit of f(x) is the same as those limits. L'Hopital's rule is used to evaluate limits that result in indeterminate forms like 0/0 or ∞/∞. For a function to be continuous, its function values and limit values must all exist and be equal for

1. Unit 2: Limits

2. What is a Limit?

3. The y-value the graph reaches as x approaches a specific value, CThe graph must approach the same y-value from both sides or the limit does not exist

4. Squeeze Theorem

5. if f(x) ≤ g(x) ≤ h(x) when x is near a (except at a) and then,

6. often with trig problems likeL’Hopital’s Rule

7. Limits that simplify to or =

8. Continuity

9. For a Function to be Continuous…All function values existAll limit values existThe function values for every x equal the limit values for every x

10. Intermediate Value Theorem

11. If f is continuous on [a,b] a value c exists such that