This is a classroom activity designed to practice finding finite limits. I decided to change the format from "I have, who has" to "WE have, who has..." because I love collaboration in my classes, and I find that the traditional "I have who has" can sometimes take too long.
The limits will all result in an initial 0/0 answer, and will need to be rewritten using one or more of the following concepts: factoring, sum and difference of cubes, rationalizing the denominator, and knowing the rule for the limit of sin(x)/x as x approaches zero. (You could also use this activity after teaching L'Hopital's Rule.)
This is a great starter, a great formative assessment, and a great way to get students to practice reading the problems aloud.