This slideshow presentation defines limits and discusses continuity, discontinuity, limits to infinity, and taking limits algebraically. It explains that a limit is the value a function approaches at a point, continuity means all function and limit values exist while discontinuity means a function or limit value does not exist at a particular point. It also outlines rules for determining limits to infinity based on exponents and describes taking limits algebraically by substitution and simplification.

1. Limits This slide show presented by: Caroline Newton

2. What is a Limit?

4. Continuity~ The continuous graph ~

5. No OR Asymptotes All function values exist All limit values exist The function values for every ‘X’ = the limit values for every ‘X’

6. Discontinuity~ The discontinuous graph ~

7. A function value does not exist A limit value does not exist A function value does not equal the limit value at a particular ‘X’ value. BREAKZ!!! ASYMPTOPEZ!!! HOLEZ!!!

8. Limits to Infinity

9. Greatest exponent in den. = 0Greatest exponent equal = ratio of coefficientsGreatest exponents in num. = infinity or neg. infinity

10. Algebraically

11. The Substitute… SIMPLIFY if you can Table of values OR graph