How to Calculate a Basic Limit

Step-by-Step Guide

1. 1

   Step 1: Plug in X-value and see if it returns a limit.

   This can be done algebraically by factoring the numerator.
   
   It can also be done by multiplying by the conjugate and then simplifying. , When an undefined answer is returned, this means there is either a hole or an asymptote on the graph.
   
   An undefined answer of 0/0 means there is a hole in the graph.
   
   This occurs when there is a common factor in the numerator and the denominator.
   
   On the other hand, if the undefined answer is c/0 where “c” is a constant, then this means there is a vertical asymptote.
   
   An asymptote is a value that the graph gets closer and closer to but never actually gets to. , By graphing the equation on a calculator, it gives you a visual representation of the limit.
   
   This should not be relied on to solve the limit, but once you arrive at the answer it can help you to be sure your answer is correct.
   
   The example in step 3 was used in the graph pictured.
   
   As you can see, the graph at x=2 has no “y” value given.
   
   This means that there is a hole in the graph, just as stated in step
   3.
2. 2

   Step 2: If 0/0 is returned

3. 3

   Step 3: see if the equation can be simplified.

4. 4

   Step 4: Check the function for holes and asymptotes.

5. 5

   Step 5: Graph the function on a calculator and check the answer.

Detailed Guide

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