the domain of an expression is the set of all input values (usually, and in this case, x-values) for which the function is defined. that is, what values can we plug in and actually get an answer.
it is often easier to find the values which do not work, and say the domain is all values but those values.
useful facts: rational functions, that is, functions that look like fractions are defined wherever the denominator is not zero. that is, the domain of a real function is all real x such that . there are several different notations in which you can express the domain. you should know what your professor requires.
squareroot functions are defined where what is squarerooted is greater than or equal to zero. that is, the domain of the function is all real x such that
put those two together to find the domain of the given expression
do you mean to find the limit as ? question: is x = 0 in the domain of the function? how do we find the limit if this is the case? what if i asked you to find , what would you do?and calculate it's limit when it's 0