# Calculus

### Derivative Rules

Derivative Rules We know that if $displaystyle y=f(x)$ then the derivative is defined to be $displaystyle f'(x)=underset{{hto 0}}{mathop{{lim }}},frac{{f(x+h)-f(x)}}{h}$ Some notions we use when we write the derivative are: $displaystyle y’=f'(x)=frac{{df}}{{dx}}=frac{{dy}}{{dx}}$ Determining the derivative of a function using the definition sometimes it  requires a lot of work and it’s easy to make mistakes so […]

### Theorems on Limits

Theorems on Limits It can be rather tedious to apply the $displaystyle varepsilon$ and $displaystyle delta$ limit test to individual functions. By remembering some basic theorems about limits we can avoid the some of this repetitive work. We shouldn’t forget that if a limit exists it is always unique.  “The Uniqueness of a Limit” […]

### Introduction to Limits

Introduction to Limits Numerical and Graphical approach to limits Numerical Approach Let’s take a function f(x) and see how the values of the functions change when x takes values closer to a specific number. Example: Let f(x)=3x+1 and calculate f(x) as x takes values closer to 1, but not exactly the value at 1. We first […]

### The Limit of a Function

The limit of a function Let f be a function and let c be a real number. We do not require that f be defined ar c but we do require that f be defined at least on a set of the form (c-p,c) U (c,c+p) with p>0). To say that $displaystyle underset{{xto c}}{mathop{{lim }}},f(x)=l$ is […]