Expert Answers
mathsworkmusic eNotes educator| Certified Educator

We have `sqrt(2)/((3a))`

` `Assume `a` is a variable and can take the value of any real number

If `a>0` this is positive

If `a<0` this is negative

As `a -> 0` from the left `sqrt(2)/((3a)) -> -oo`

As `a -> 0` from the right `sqrt(2)/((3a)) -> oo`

As `a -> oo` `sqrt(2)/((3a)) -> 0` from the right

As `a -> -oo` `sqrt(2)/((3a)) -> 0` from the left

The graph takes the shape of `y =1/x`:





justaguide eNotes educator| Certified Educator

It is not possible to determine the value of `sqrt2/(3*a)` as the value of a is not known and a is not a constant.

The value of `sqrt 2/(3*a)` cannot be determined unless the value of a is given.