Thursday, April 16, 2015

Advanced Math Solutions – Limits Calculator, Limits at infinity

In the previous post we covered infinite discontinuity; limits of the form \frac{1}{0}. Here we examine functions where the independent variable approaches infinity, or simply put the variable grows without bounds. Infinity is not a number, hence we cannot use the standard substitution method. Limits of the form \frac{0}{0},\:\:\frac{\infty }{\infty },\:\:\infty -\infty,\:\:\infty \cdot 0,\:\:1^{\infty } are invalid. We can try to apply algebraic manipulation to transform the limit into something we can solve (limits of the form \infty +\infty,\:\:a\cdot\infty,\:\:\infty^a,\:\:\frac{a}{\infty} ), or use more advanced techniques such as the Squeeze Theorem or L’hopital.

Let’s start with the basics (click here):

Here’s another example (click here):

Here’s an example using basic algebraic manipulation (click here):

Here’s another example using algebraic manipulation (click here):

In the next post we’ll dive into rational functions, square roots and infinity