This is Justin, unfortunately I have to do my blog on Dustin's account because for some reason I didn't get the invitation on any of my emails, but anyways...
for the first 10 days of schools we talked about limits.
In definition:
"In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of a limit allows one to, in a complete space, define a new point from a Cauchy sequence of previously defined points. Limits are essential to Calculus( and mathematical analysis in general) and are used to define continuity, derivatives, and integrals. The concept of the limit of a function is further generalized to the concept of topological net, while the limit of a sequence is closely related to limit and direct limit in theory. In formulas, limit is usually abbreviated as lim as in lim(an)=a or represented by the right arrow(->) as in an -> a" (wikipedia)
To find the limit, plug in for x to find a y value(which is a limit). Most of the time, directly plugging in gets a 0 somewhere, so you have to go further...by factoring, squeeze, graphing, chart, etc.
The chart simply works by recording the number the limit is directly approaching:
Ex. lim , you create a chart with the values that approach zero
x->0
-.1|-.01|-.001|0|.001|.01|.1
Sparky #1
ReplyDeletewell my stupid account refuses to give me the option of posting a blog so im gunna do it as a comment. So these last few weeks have been mostly limits and review. One of the most important things that we have learned has been the intermediate value theorem. The intermediate value theorem explains that if there is a graph continuous between two y values, then any value in between those two numbers has at least one x-value that, if plugged in, will result in that number.
For example: f(x)=(3x^3)-5 continuous on all x-values [1,3]
f(1)=(3)(1)-5=-2
f(3)=(3)(3)-5=4
so any value chosen between -2 and 4 will be solvable in terms of x
for example 2
(3x^3)-5=2
3x^3=7
x^3=7/3
x=3rd root of 7/3.
tada