Throwback Blog

well, it looks like I'm doin a throwback blog for now

I'll just talk about limits, because I didn't really understand the stuff from the end of the week.

let's say you wanna find the limit of an equation, such as lim ((x-3)^2)/x
x->7

You've got to plug in whatever x approaches into the equation, as long as it doesn't result in a 0 on the bottom of the equation.

So if it were x -> 0 instead of x -> 7, the answer to this problem would most likely be Ø.
If that happens, you need to do one of two things.
*note* You do this whenever the bottom would equal Ø when you plug in whatever x approaches, not just when x -> 0.

One way would be by plugging the function into a table and using numbers that are close to the x -> to find what both sides approach.
In this case, the table would be: -.1 -.01 -.001 0 .001 .01 .1
-96.1 -906 -9006 8994 894.01 84.1
So as you can see, from the left, the graph/equation is approaching -∞, and from the right, the graph/equation is approaching ∞.

Another way you could figure it out is by using arithmetic.
((x-3)^2)/x
(x^2-6x+9)/x = 0
x^2-6x+9=0
x^2-6x=-9
x(x-6)=-9
x=-9 x=6
And then you figure out which is the limit, which it usually is hard to figure out.