How do you find the limit of $((1/(x+3))-(1/3))/x$ as x approaches 0?

Question

18548 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-07T23:35:29

$((1/(x+3))-(1/3))/x |_(x to 0)$

$= ( (3 - (x+3))/(3(x+3))) /x |_(x to 0)$

$= -( ( x )/(3(x+3))) /x |_(x to 0)$

$= - ( x )/(3x(x+3)) |_(x to 0)$

$= - ( 1 )/(3 (x+3)) |_(x to 0)$

$= - 1/9$

How do you find the limit of ((1/(x+3))-(1/3))/x((1/(x+3))-(1/3))/x as x approaches 0?