Limits (Calculus)

[Goldenboko]

Limits are actually quite simple when it comes down to it. You just have to take the fancy math mumbo-jumbo and dumb it down. Limits ask where the graph appears to be going. So, for 2, you just look at it (tracing with with your finger like qwerty said) and if they both go to the same place. Limit.

The way that helped me understand what was going on though, was the numerical way of looking at a limit. When the problem says x->2, you could, numerically, look at numbers that get closer and closer to two. Here it would look something like this:

x 1.9, 1.99, 1.999, 1.9999
y .9__.99__.999___.9999

x 2.1, 2.01, 2.001, 2.0001
y 1.1, 1.01, 1.001, 1.0001

Looking at the data tables, it's pretty clear that the y value of the graph is getting closer and closer to 1 as you approach two, without knowing what the actual point on the graph is. So, even if the point on the graph was 9, it wouldn't be the limit because all of the numbers around that X Value on the graph clearly get closer to 1, not 9.

Hope my way of learning this helped.

EDIT: The Professor can try and trick you with left and right side limits, these are denounced with a positive or negative mark for an exponent after the x approaches (ex: x->3^-). I'm fairly sure negative is a right-sided limit (limit on the right of the graph approaching the left of the graph) and a positive is a left-sided limit (limit on the left of the graph approaching the right of the graph). Also if the graph looks like it's approaching infinity, like this only both graphs going straight up or down:



There is no limit, if you think about it logically it doesn't make sense for a point on the graph to equal infinity as infinity is not a set number.