The limit actually exists! (sometimes)
As you can guess, this week in class (after we finished the review and its test), we reviewed and learned about limits. Limits describe the behavior of a function as the input approaches a certain number. What use do they have? Now, most people would answer "none" here, but I, being in this class, have to say that limits are in fact important because they serve as the base for a lot of calculus. After all, describing how functions and curves behave is a big part of this class.
The ideas of limits and limit properties are based on information about graphs and graph behavior that we learned in Pre-Calculus. Since this week we specifically talked about the basic definition of limits, limits from the left and the right, and the Sandwich theorem, I think we are going to discuss limits as x approaches infinity next, or end behavior. I could be completely wrong, of course, but this is my best guess.
I definitely understand the fundamentals of limits very well, especially determining whether a function has no limit. If a function has no limit as the input approaches a certain value, it has to have one of three things at the value. Either the function has a asymptote at the number with the two ends of the function going in opposite directions, it oscillates, or opposite ends of the functions are approaching different values. The important thing to keep in mind is that holes do not necessarily mean no limit. Limits are not defined by functional value but rather what value the function gets closer to in as x gets closer to a certain value.
One thing that I did not understand so well this week was the Sandwich Theorem. I suppose I just need to hear someone explain it to me and show me an example rather than just reading the book notes. I have found this video by Khan Academy explaining it, though. I have not seen it yet, but Khan Academy usually has really good educational videos. Overall, I think my participation this week has been good and, while there are some topics that I might need to review, there is nothing in particular that I need to work on.
As you can guess, this week in class (after we finished the review and its test), we reviewed and learned about limits. Limits describe the behavior of a function as the input approaches a certain number. What use do they have? Now, most people would answer "none" here, but I, being in this class, have to say that limits are in fact important because they serve as the base for a lot of calculus. After all, describing how functions and curves behave is a big part of this class.
The ideas of limits and limit properties are based on information about graphs and graph behavior that we learned in Pre-Calculus. Since this week we specifically talked about the basic definition of limits, limits from the left and the right, and the Sandwich theorem, I think we are going to discuss limits as x approaches infinity next, or end behavior. I could be completely wrong, of course, but this is my best guess.
I definitely understand the fundamentals of limits very well, especially determining whether a function has no limit. If a function has no limit as the input approaches a certain value, it has to have one of three things at the value. Either the function has a asymptote at the number with the two ends of the function going in opposite directions, it oscillates, or opposite ends of the functions are approaching different values. The important thing to keep in mind is that holes do not necessarily mean no limit. Limits are not defined by functional value but rather what value the function gets closer to in as x gets closer to a certain value.
One thing that I did not understand so well this week was the Sandwich Theorem. I suppose I just need to hear someone explain it to me and show me an example rather than just reading the book notes. I have found this video by Khan Academy explaining it, though. I have not seen it yet, but Khan Academy usually has really good educational videos. Overall, I think my participation this week has been good and, while there are some topics that I might need to review, there is nothing in particular that I need to work on.