Algebra vs. Calculus

1. What is the DIFFERENCE between finding the limit of a function at x = c and actually plugging in the number x = c? When are the two cases the SAME.

~Finding limit at x=c, you are finding outputs that approach "c", your finding the "y" values of f(x)as x is approaching c. There can be a "hole" or what we call a "Removable Discontinuity", this "hole" can be covered with a piecewise function.
~When plugging in number x=c, there is an exact point. There is no "hole". You are finding the output(y) when x is equal to a constant.
-The two are the same when you take the limit of f(x) as x approaches "c".


2. What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?

~Change of Y divided by the change of X is the same when you are finding the slope of either one.

~Finding slope of a derivative involves many complicated equations of how to find tangent and secant lines, using LIMITS/: ,with using equations like that one below.../:


~Finding the slope of a line is easy, all you need to do is find the RISE/RUN...
In other words, find the change of Y over the change of X.

Limits

Sorry for posting this up late Ms.Hwang I thought i had posted it up earlier...(:
oooopppps.(:

At first the sine functions were confusing
but when Ms. Hwang(you) explained to me it was more clear, i thought the limit when x aproaches 0 was the same as when the limit aproaches infinity.
Now i know the difference(:
I wont forget(: lol!

The piecewise functions are a little more challenging because there is more than one equation in the problem, making the problem that much harder.
Those problems are pretty hard and i would apprectiate more help on them(:

Problems i also get stuck with is like #5 on p.95
when the limit aproaches 0.... and it is the denominator.
that confuses me.. with the extended functions....?
Gosh../:
I need help(:
and would appreciate some(: