Limits!
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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 states that the sign after the number being approached indicates the side of the graph and discusses factors that do and do not cancel in determining asymptotes or holes.
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Limits!
- 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. HolesAKA : 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
- 13. Factors that don’t cancel in the denominator
- 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