Use formal definition of limits to show:

[studentCal]

Hi, Could somone please show me how i prove this spesific function. im pretty stuck on it

Use the formal definition of limits to show:

 

[pka]

Use the formal definition of limits to show:
View attachment 1381

Note that \(\displaystyle |2x^2-4x-6|=2|x+1||x-3|\).
You have control over the factor \(\displaystyle |x-3|\) because \(\displaystyle x\to 3\).

So proceed.

 

[studentCal]

Is it possible to do it like this?

 

[pka]

View attachment 1382
Is it possible to do it like this?

Start by stipulating that \(\displaystyle 0<\delta<1\).
Then if \(\displaystyle |x-3|<\delta\) then \(\displaystyle |x+1|<5\).

 

[studentCal]

im abit confused, where did you get 5 from?

 

[pka]

im abit confused, where did you get 5 from?

If \(\displaystyle |x-3|<1\) then \(\displaystyle |x+1|<~?\)

 

[studentCal]

ah i see.

so basicly that gives me delta = epsi /5

and i rewrite it ect...?

btw: thanks for help pka