Question

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

Answer 1

`((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`