InteGreat
Activity
Teacher should start with a review of limits, infinity, and derivatives to prepare students for the upcoming lesson. Teacher can ask discussion questions, for example:
- What does it mean to take the limit of a function?
- How can we find the area under a line, such as y=x?
- How can we find the area under a graph which does not have straight edge?
- How can we calculate the area between the function and the x-axis from 0 to 5?
- Could we use the same sort of triangle to calculate the area under the function from 0 to 10?
- What shape would the area under the line be from 5 to 10?
- Can we find the area under any straight line with a trapezoid?
- What will happen if we divide the curve into lot of little line segments to find its area?
- Is the straight line a very good approximation of y=x^2 from 0 to 5? How about 0 to 10?
- Are these lines a better approximation of y=x^2 from 0 to 5? Why?
- What do you think will happen if we increase the number of partitions to 10 or more?
- Which method give best approximation? Why?
- How could we calculate the area under the curve using these lines?