Continuity is a concept in calculus that deals with graphs, it means that there is something that goes on (continues) without being interrupted. Discontinuity is along the same lines, but instead of being continuous, it is interrupted by jumps, holes and breaks in the graph.
<----CONTINUITY
<----DISCONTINUITY2.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 graph/function. The limit exists only when the right and left limits are equal. On the other hand, the limit does not exist if the graph has a break (jump, oscillating, infinite discontinuities). The difference between a limit and a value is that the value is the number that belongs and appears in the graph.
3.How do we evaluate limits numerically, graphically, and algebraically?
Numerically: create a table that has x-values and function of x values, use the number that the limit as x approaches, which is what we will find. Write it mathematically (limx-x>#f(x)=).
Graphically: analyze given graphs. Notice if sides do not meet, a limit does not exist. If the graph has discontinuity, the limit is there. Jumps, oscillating and infinite discontinuities = DNE.
Algebraically: we use direct substitution, dividing out or factoring method, rationalizing/conjugate methods.
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