| Line 36: | Line 36: | ||
The definition of a continuous function is that the limit at any point is equal to the value at that point. | The definition of a continuous function is that the limit at any point is equal to the value at that point. | ||
| − | The complicated math way to say this is <math> \lim | + | The complicated math way to say this is <math> \lim{x\to x_0}f(x)=f(x_0) </math> |
This makes sense. If a function is continuous then every point is exactly where we would "expect it to be". | This makes sense. If a function is continuous then every point is exactly where we would "expect it to be". | ||
Revision as of 23:38, 31 October 2017
Work in Progress
Limits Approaching Infinity Intuitively
by Kevin LaMaster, proud Member of the Math Squad.
Introduction
I've noticed that many calculus one students loathe taking limits specifically as they approach infinity. This series should not be an introduction to limits nor should it replace a strict definition for a limit. Both of those can be found better at this tutorial. This only serves for a crash course tutor replacement for Calculus 1 students struggling with some difficult homework.
Basic Limits
Just as a recap over basic limits not into infinity.
Limits of Continuous functions
For the majority of limits the limit can just be found by plugging the values into the function.
For example $ \lim_{x\to 2}x^2+2x+1=2(2)^2+2(2)+1 $
The definition of a continuous function is that the limit at any point is equal to the value at that point.
The complicated math way to say this is $ \lim{x\to x_0}f(x)=f(x_0) $
This makes sense. If a function is continuous then every point is exactly where we would "expect it to be".
