A discontinuity is a function with a hole, an asymptote, a jump, or oscillating behavior.
2. A limit is the intended height of a function. A limit exist when the intended height approaching from the right and left are the same. A limit doesn't exist when you get different intended heights approaching to the left and approaching to the right. The difference from a limit and a value is that even if you have a hole (which is the value) on the intended height it will still be a limit, but its value wont be .
3. We evaluate limits numerically we will get x-values really close to the original "x" from both the right and the left. There we will see if the intended height will be the same , which will tell us if we have a limit or not.
To evaluate limits graphically we look at the graph, we look at the point as x approaches whatever from the right and the left, from there we can conclude if its a limit or not.
To evaluate limits algebraically we simply just substitute the x approaches to the function. However sometimes it might not work so we use factoring, if that also fails we multiple by the conjugate.
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