This week, we focused more on limits and continuity. I think that we have learned and practiced with continuity has helped me strengthen my understanding of limits. I remember learning about both limits and continuity last year, but I don't think we ever covered the topics in this much depth.
I was pretty excited to start studying limits this year but they have turned out to be very different than what I had expected. Last year, limits were very easy to find with the press of a few buttons on a calculator. But now that we are learning how to find limits algebraically, I am glad that I have a much deeper understanding of what limits are and how to find them.
What we learned about continuity this week is mostly new and I really like how we are using specific definitions and rules to determine if a function is continuous. I have found the three prong test really helpful and I use it whenever I can. I liked the activity that we worked on in class on Thursday where we tried to come up with solutions to four different problems involving the three prong test. I liked being able to work on solving the problems in our groups and then being able to share our ideas and hear other groups' solutions. This activity and discussion really helped me to understand continuity and how to tell if a function is continuous with the three prong test. When testing a function for continuity, I know that I need to look to see if f(c) is defined, if the limit of f(x) as x approaches c exists, and if the limit of the function at x equals the functional value of x. I know that if a function passes all three of these tests, the function is continuous, but if one or more is broken, there is discontinuity.
I was pretty excited to start studying limits this year but they have turned out to be very different than what I had expected. Last year, limits were very easy to find with the press of a few buttons on a calculator. But now that we are learning how to find limits algebraically, I am glad that I have a much deeper understanding of what limits are and how to find them.
What we learned about continuity this week is mostly new and I really like how we are using specific definitions and rules to determine if a function is continuous. I have found the three prong test really helpful and I use it whenever I can. I liked the activity that we worked on in class on Thursday where we tried to come up with solutions to four different problems involving the three prong test. I liked being able to work on solving the problems in our groups and then being able to share our ideas and hear other groups' solutions. This activity and discussion really helped me to understand continuity and how to tell if a function is continuous with the three prong test. When testing a function for continuity, I know that I need to look to see if f(c) is defined, if the limit of f(x) as x approaches c exists, and if the limit of the function at x equals the functional value of x. I know that if a function passes all three of these tests, the function is continuous, but if one or more is broken, there is discontinuity.