A continuity is when you can draw a graph with out and holes, jumps, unbounded behavior like shown in the second picture.
A discontinuity is when you have a graph with jumps , holes, or unbounded behavior. Like in the first picture it is s jump with holes.
2 What is a limit? When does a limit exist? when does a limit not exist? what is the difference between a value and limit ?
A limit is when you plug in x in to the equation.
A limit exist when two things have the same point.
A limit does not exist when they end up at different points like picture 1
A limit is not always on the graph but its what you expect. a value is what your really looking for.
3 How do we evaluate limits numerically, graphically, and algebraically ?
solving limits numerically is very easy. first you need to draw a table with 14 squares in two rows. on the top 7 rows you want to write down the values that you will be plug in to the equation.to find the answers.so solve it graphically we want to the limits. so we look at the graph and determan where everything is by looking at the points and derection of the graph. To solve it algebraically you have three ways of finding them. first is the substitution method witch is when you plug in 0 and see what you get. you can eather get a number , zero, undefined , there is also the factoring method witch simplifyes the equation and then use substitution method agian. and there is also the last one witch is conjugate is when you times it by the conjugate so it simplifies out.
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