Calculus Methods

01 Finding Domains

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         1)  Rewrite function as a single fraction, and factor the denominator.

         2)  There are only three rules:

                  A)  No negative numbers are allowed inside square roots.

                  B)  No zeroes are allowed in the denominator.

                  C)  No non-positive numbers are allowed inside logs.

         3)  Write separate domains for each item involved in the function.

         4)  Combine the separate domains using "and."

         Example:  Find the domain of

         1)    

         2A)  There is only one square root (it occurs twice):

         2B)  There are two factors in the denominator:

         2C)  There is one logarithm:

         3)  The four domains for this example problem are thus:

    4)  The single domain that is commensurate with all of

    the above domains is (it might help to draw a number

    line):