Question

How does `\lim_(n\rarr\infty)(2|x-2|)/(n+3)=0`?

Without doing any further work, is it possible to recognize the limit as 0?
Or should I simplify further (if so, then how?)

Answer 1

show below

Explanation:

show the steps and focus in the explanition

since `nrarroo` n is a variable value and others like: x are constant

x=constant

any constant divide by`oo`equal zero

c=any constant
`c/oo=0`

`c/-oo=0`

in addition any constant plus `oo` or `-oo` equal
`c+(+oo)=oo` and
`c+(-oo)=-oo`

`lim_(nrarroo)[(2|x-2|)/(n+3)]=(2|x-2|)/(oo)=0`

`(2|x-2|)=`constant

`lim_(nrarroo)[(2|x-2|)/(n+3)]=0`