¿¡Que Dijo!?

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?

• When you're looking for the limit of a function at x = c, you're looking for the closest output (y) as x gets closer and closer to the constant from both sides
  
• When you actually plug in the number x = c, you're looking for the exact output at the constant
  

Ex: f(x) = int x

The lim f(x) as x->2+ is 2, but the lim f(x) as x->2- is 1
The lim f(x) as x-> 3/2 is 1

• Both cases are the same when the lim f(x) as x->c = f(c). In other words, both cases are the same when the function is contiunous, because the limits from the positive and negative sides of the constant are the same as the limit when you plug in x=c .
  

Ex: f(x) = 1/xThe lim f(x) as x->0=0, lim f(x) as x->1=1, lim f(x) as x->-1=-1, e.t.c.

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

• The main similarity between finding the derivative and finding the slope of a line is that you basically use the same formula:
  

m = change of y/change of x which is also known as (y2-y1)/(x2-x1)

• When you're finding the derivative, you are looking for the slope of the tangent line for that specific point as h approaches 0, although there are plenty of other ones that could be found on the same curve of the graph..
  
• When you're finding the slope of a line, you are finding the slope one specific line unlike when you're finding the derivative...