### TJ: CA I.9 Introduction to Limits

#### Introduction to Limits

I have found students generally enjoy this activity and find it more
concrete than the work that they have just done on rate of change
equations. They struggled with Q3 in general and part (d) in particular.
I think because the find it hard to believe that any exponential
function will dominate any power function. It is also difficult because
they are asked to generalize by themselves which is always a difficult
step. It is good to talk to small groups during this process and to have
a whole class discussion when everyone has worked on it. If this is
where you break to send them away (which is appropriate so that students
have time to think about this question) it is a good idea to ask
students to formulate a plan for part (d) before leaving the classroom.
Students struggle again with Q7 where they are being asked to reason
algebraically from a set of statements that we are taking to be true
about how sums of functions behave and which types of functions dominate
in the long term. I think it can be helpful to discuss this question in
class and ask a number of students to explain their reasoning process. |

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