A continuity is a function that does not have any breaks, holes, or jumps on the function. It is predicatable and we can draw it without lifting a pencil from a paper. A discontinuity is the exact opposite, it has a break, a hole, a jump and is drawn with lifting a pencil from the paper. There are 3 different types of discontinuities; point discontinuities, jump discontinuity, oscillating behavior and infinite discontinuities.
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| http://www.conservapedia.com/Continuous_function |
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| http://www.conservapedia.com/Continuous_function |
What is a limit? When does a limit exist? When does a limit not exist? What is the difference between a limit and a value?
A limit is the intended height of a function and exists in removable discontinuities and continuous graphs. A limit does not exist at a jump, oscillating or infinite discontinuity because the intended height is never reached. A limit is the intended height, whereas the value is the actual height.
How do we evaluate limits numerically? Graphiclly? Algebraiclly?
We evaluate limits numerically on a table. We evaluate limits graphically on a graph, were left and right meet in the middle. And algebraically using the substitution method, the dividing/factoring out method and the rationalizing/conjunction method.
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