Limits of functions - Rhea

Tutorial Template

by: Michael Yeh, proud Member of the Math Squad.

 keyword: tutorial, limit, function, sequence 

INTRODUCTION Provided here is a brief introduction to the concept of "limit," which features prominently in calculus. We first discuss the limit of a function at a point; to help motivate the definition, we first consider continuous functions. Unless otherwise mentioned, all functions here will have domain and range $ \mathbb{R} $, the real numbers.

Continuous functions

Let's consider the the following three functions along with their graphs (in blue):

$ \displaystyle f(x)=x^3 $

$ g(x)=\begin{cases}-1 &\text{if}~x<0\\ 1 &\text{if}~x\geq 0\end{cases} $

$ h(x)=\begin{cases} \sin\left(\frac{1}{x}\right) &\text{if}~x\neq 0\\ 0 &\text{if}~x=0\end{cases} $

TOPIC 3

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TOPIC 2

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REFERENCES

[1] "Loream Ipsum" <http://www.lipsum.com/>.

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