Question

How do you find the limit of `(sqrt(6) – sqrt (5h^2 + 11h + 6)) / (h)` as h approaches 0?

Answer 1

`-11/(2sqrt(6))`

Explanation:

`((sqrt(6) – sqrt (5h^2 + 11h + 6)) / (h))( (sqrt(6) + sqrt (5h^2 + 11h + 6)) /(sqrt(6) + sqrt (5h^2 + 11h + 6))) =`

`(6-(5h^2+11h+6))/(h(sqrt(6) + sqrt (5h^2 + 11h + 6))) = -(5h+11)/(sqrt(6) + sqrt (5h^2 + 11h + 6))`

then

`lim_(h->0)(sqrt(6) – sqrt (5h^2 + 11h + 6)) / (h)=-11/(2sqrt(6))`