Continuity is when there are no jumps, breaks, or holes. You can draw the line without having to raise your pencil. The limit and value have to be the same. A discontinuity is when there is a jump, break, or hole. There are different types of them jump, point, infinite, and oscillating.
2. What is a limit?
A limit is the intended height of the function.
When does the limit exist?
The limit exists when you reach the same height from the left and the right.
When does the limit not exist?
The limit does not exist when you don't reach the same intended height from both the left and the right or when you have a jump discontinuity and have the closed circle above the open circle.
What is the difference between a limit and a value?
The difference is that a limit is the intended height of the function the value is the actual height of the function.
3. How do we evaluate limits numerically, graphically, and algebraically?
Numerically is when we use a table chart to help us evaluate the limit we pick a number and get closer to it from the left and the right. Graphically is when we use a graph as a visual and use our fingers to see if the limit has the same left and right. Algebraically is when we use substitution, division, factoring,and rationalizing to help us evaluate the limit.
