Limits

Limits

1. We say a function has a limit as x approaches c if from both sides of this x the y-value coincides into the same number.

   • Limits can be determined using three methods:
     • Numerically
       • Limits can be determined numerically by making a table of values
         • Looking at a function, we should determine two numbers terribly close to your c from the right.
           • Then we should determine two numbers also terribly close to your c from the left.
             • Next, we create the table, for example:
               • x = c.99, c.999, c, c.001, c.01
                 • Plugging in our values, the number they all approach is our limit.
     • Graphically
       • Limits can be determined graphically by looking at a graph or graphing a function and:
         • Checking what number the graph approaches from one side,
           • checking the same thing from the other, and
             • Asking the question: "Are these numbers the same number?"
               • If they are, that number is your limit.
                 • If they aren't, the limit does not exist.
     • Algebraically
       • When you substitute your c in a function and the product is undefined, then we should perform an algebraical operation to solve it.
         • To solve algebraically, you should simplify the function until something cancels out; a hole
           • Now, when plugging in c, we should get a number.
             • That's the limit.