This document defines and explains key limits concepts in mathematics including intended height, approaching a limit from the right or left, holes, asymptotes, vertical asymptotes, horizontal asymptotes, and slant asymptotes. It provides descriptions of each concept and notes characteristics like signs in equations or factors that do or do not cancel in determining different types of limits and asymptotes.

1. LIMITS!!!!!!! By: Glenn Sincovich

2. Intended Height =

3. The y value that is approached as X approaches a certain value

4. Approaching from the Right

5. Has a + sign in the equation after the number that X is approaching, and this means that you look at the graph COMING from the right side, or the positive side.

6. Approaching from the Left

7. Has a - sign in the equation after the number that X is approaching, and this means that you look at the graph COMING from the left side, or the negative side.

8. Holes AKA : Points of Discontinuity

9. 1. Factors that cancel in the denominator2. If everything in the denominator cancels, there are NO asymptotes, just a hole (or holes)

10. Asymptotes

11. A line that the graph approaches but never touches

12. Vertical Asymptotes

13. Factors that don’t cancel in the denominator

14. Horizontal Asymptotes

15. 1. When the greatest exponents are equal: take the ratio of the coefficients2. When the greatest exponent is in the denominator, y=0

16. Slant Asymptotes

17. When the greatest exponent is one more than the numerator: use long or synthetic division