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There are three methods of evaluation.
We will use the function y=(x^3-x^2)/(x-1).
The first method is direct substitution. It is exactly as it sounds.
This will not work though in this case, for finding the limit as X approaches 1, because the graph has a hole there.
You can factor this equation though. This leads to x^2(x-1)/(x-1). The like terms cancel leaving x^2 which leads to 1.
The next method involves creating a table which gets closer and closer to the actual value.
The final method of evaluation is to look at the graph, which is easy, but unavailable in almost all cases.
Evaluate the limit using all three methods. Keep in mind, the limit may not exist.
1. y=(x^3-8)/(x^2+2x+4) as x approaches 1.
2. y=(x-4)^2/(x-2) as x approaches 2
3. y= 1/(x^2-4) as x approaches 2.
We will use the function y=(x^3-x^2)/(x-1).
The first method is direct substitution. It is exactly as it sounds.
This will not work though in this case, for finding the limit as X approaches 1, because the graph has a hole there.
You can factor this equation though. This leads to x^2(x-1)/(x-1). The like terms cancel leaving x^2 which leads to 1.
The next method involves creating a table which gets closer and closer to the actual value.
The final method of evaluation is to look at the graph, which is easy, but unavailable in almost all cases.
Evaluate the limit using all three methods. Keep in mind, the limit may not exist.
1. y=(x^3-8)/(x^2+2x+4) as x approaches 1.
2. y=(x-4)^2/(x-2) as x approaches 2
3. y= 1/(x^2-4) as x approaches 2.