Calculus Course/Change in Variable

Change in VariableEdit

A Change in variable is a term used to express the diffeence between 2 variables . Let ${\displaystyle \Delta }$  represents Change in 2 variables ${\displaystyle x_{0}}$  and ${\displaystyle x}$  then

${\displaystyle \Delta x=x-x_{0}}$
${\displaystyle x=x_{0}+\Delta x}$

If there is a function ${\displaystyle f(x)}$  such that when ${\displaystyle x}$  change by an amount ${\displaystyle \Delta x}$  the change in function will be

${\displaystyle \Delta f(x)=f(x)-f(x_{0})}$
${\displaystyle f(x)=f(x_{0})+\Delta f(x)}$

ExampleEdit

There are 2 points (1,3) (5,7) then

${\displaystyle \Delta x=x-x_{0}=5-1=4}$
${\displaystyle \Delta f(x)=7-3=4}$