So this is my first blog of the year, and I'm already three days late on it....but I don't really care because I can almost bench press 300 pounds now. So, Limits:
-When determining if a limit exists on a graph all you really do is check to see if both sides of f(x) are approaching the same thing. If both sides are approaching the same thing, then the limit is whatever number you get. If both sides do not match up, then the limit does not exist. It's that easy.
-A jump on a graph will NEVER have a limit
-An asymptote will SOMETIMES have a limit
-A removable will ALWAYS have a limit
-When you do not have a graph you just plug in what (x) is approaching. When you can not plug in then you use algebra or trig so that you can plug in (x).
Ex.
lim (x^2+x+2)/(x+1)
x->1
Plug one in for (x) and solve. You should get 4/2, which simplifys to 2. The limit is 2.
One thing I seem to have trouble with is simplifying the problems with Delta(x) in them. No matter what the problem is I always do something wrong and get the whole thing wrong...like number 16 on page 79. I'm lost on how the answer ends up being 2x+1........
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