The whole concept of limits is something that I've never really understood. I first learned about limits in pre-calculus, but did not understand how they worked or even what they were. I did not know that there were different types of limits. I didn't realize that approaching a number from either the left or right side of that number could possibly yield a different limit. I also didn't know that the limit of a function only exists if both of the one-sided limits exist and are equal.
Real life example of a limit: compounding interest rates. This is an example of a limit because as the rate is continuously compounded it only adds a very small amount of money to your bank account. To actually make a significant amount of money from the interest alone, that money would have to sit untouched for an extremely long time because the amount compounded each time is so small.
Problems:
1. Decide whether the limit as x approaches 0 of cos3x / x exists or does not exist. If it exists, find the limit.
Using the table method for finding a limit I found that this limit does not exist. When approaching x from the right and from the left the limit does not exist.
2. What is the limit of 2x+4 as x approaches 2?
The limit is 8. This function is continuous, because is it is a linear function, therefore you can just plug 2 in for x to solve the equation.
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