Wellllll we are in calculus now and for the first 2 weeks we have been relearning what we learned at the end of advanced math. We have relearned everything about limits. We have learned continuity and numerical limits. Sooo i guess im going to talk about these things now.
CONTINUITY
Continuity basically means where does the graph exist and stuff like that. There are a couple things that make a graph not exist in some areas. These things are removables, verticle asymptotes, jumps, etc. I cant put a picture of a graph on here but i will describe these things the best i can. A removable is basically a hole in the graph. It should look like a little unfilled in hole. A vertical asymptote would look like two lines going up or going down at a certain number. These can do one of two things. They can either both be going the same direction or they can be going two different directions (the directions being either up or down). If these two match going one way then it can equal either infinite or negative infinite. Of course infinite means they both go up and negative infinite means they both go down. Last but not least there is a jump. A jump is where there are two graphs and when they get to a certain number they both stop. So lets say there is a graph of five. When the graph of five stops attttt 2, a graph of -3 may start the other way. That is probably really hard to understand but its the best i can do.
NUMERICAL LIMITS
Well a numerical limit is basically when you need to use the chart that we learned. The chart should subtract (from left to right on the chart) .1 , .01, .001 , then it should add .001, .01, .1 . You should add and subtract these numbers from the number you are using to plug into the limit.
Lets say you have a limit at x approaches 3 of x^2+2x+4. Now plug into the graph. The graph should come out saying (from left to right)
18.21 18.92 18.992 x 19.008 19.08 19.81
from the left going to the middle these numbers are approaching 19. Now from the right approaching left they are also approaching 19. So the limit of this equation is 19. You dont always have to use the graph. You only use it if you plug in and get undefined. I showed you that as an example because it was easy. Anyways, thats all i really have to say for now. So good luck in calculus ap everyone. I know ill need it.
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