it does take a lot of patience to deal with the inner bully, but i have been forming new thought that work on uprooting the inner bully when it is there. i imagine the inner bully as a weed and i get a shovel and i uproot it, the holes left there are annoying b/c the inner bully goes back and tells me that i have limitations that make me a bad person, so i fill those holes with flowers. i am creating a garden in my mind of flowers. i like solving limits algebraically than using the graphs or tables. graphs and tables are still a bit confusing, but they’re starting to make sense. a limit is “is the value that a function or sequence “approaches” as the input or index approaches some value.”

so the limit as x–>0 of 5 is 5 since as x is approaching zero, the function is getting closer to 5. finding limits with sine, cosine or square roots and fractions is a bit more complicated b/c sometimes they have undefined values or the limit does not exist such as in this case: lim x–>0 of 1/x. if you were to plug in zero for x, it would be undefined. however with limit problems, you should always check to see if there is another way to solve them b/c some functions do have limits that you have to solve for a finite value.
this is the basic idea of limits, but they get more complex as you have to graph them b/c sometimes their is an open circle for the points that are not continous and a closed circle for the ones that are. limit values have many different graphs as long as it follows the rules, which is one thing that i am still working on.
arrow means approaches