We learned about derivatives a lot this week and what we can predict about the graph of f' when looking at the function f, such as maximums and minimums corresponding to zeroes on the graph of the derivative. Also, the points of highest slope on the original function f correspond to the maximums and minimums on the derivative function. The difference quotient which we now know as the derivative is used to determine slope at a point which from a direct approach using zero as the movement is impossible, but using a value very near zero will tell you the slope at the point, assuming there is rate of change at a point.
This week we learned the difference between a hole, a limitless point, horizontal asymptotes which is as a limit approaches infinity and vertical asymptotes. We kind of knew all of this, but review is helpful for those of us who forgot or did not care the previous year. Specifically, when the limit approaches negative infinity from one direction and infinity from its counterpart, there is no limit. We also learned the three rules of limits which are quite helpful when having to prove algebraically whether or not a limit exists.
Limits are defined as the value that a certain input seems to equal based on similar inputs. This means that while looking at a graph that seems to approach a point, even if it is a piece-wise function and is actually elsewhere, what it looks like is what the limit equals. Limits are very useful for identifying the value of holes in functions because of dividing by zero. However, limits do not exist at certain points in graphs because of asymptotes where the graphs head in opposite directions (To infinity, To negative infinity).
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Gavin RoupeChess Expert, interested in Psych and fun ArchivesCategories |