Wednesday, February 25, 2015

Advanced Math Solutions – Limits Calculator, the basics

The limit of a function is a fundamental concept in calculus concerning the behavior of that function near a particular point.  Limits help us approximate functions for any point x even if the function itself does not exist at that point (to infinity and beyond).

We will start with the substitution method (a.k.a the plug-and-chug method).  Plug in the value to which x is approaching (can’t get easier than this).  The limit is simply the function value.  Pay attention, this method works for limits that involve continuous functions only.

The following limit properties can be useful:

If the limits of f(x), g(x) exist, then:

  • \lim_{x\to{a}}[f(x)\pm{g(x)}]=\lim_{x\to{a}}{f(x)}\pm\lim_{x\to{a}}{g(x)}
  • \lim_{x\to{a}}[f(x)\cdot{g(x)}]=\lim_{x\to{a}}{f(x)}\cdot\lim_{x\to{a}}{g(x)}
  • \lim_{x\to{a}}[c\cdot{f(x)}]=c\cdot\lim_{x\to{a}}{f(x)}
  • \lim_{x\to{a}}[\frac{f(x)}{g(x)}]=\frac{\lim_{x\to{a}}{f(x)}}{\lim_{x\to{a}}{g(x)}},\:where\:\lim_{x\to{a}}{g(x)}\neq{0}

Lets start with a simple example (click here):

Here’s another example involving product (click here)

One more example involving quotient  (click here):

That was a breeze.  In the next post we will continue with discontinuous functions