`lim_(x -> oo) (5 - 2x^(3/2))/(3x^(3/2) - 4)` Find the limit, if possible

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the limit, hence, you need to replace `oo` for x in equation:

`lim_(x->oo) (5 - 2x^(3/2))/(3x^(3/2) -4) = (5 - oo)/(3oo - 4) = -(oo)/oo`

Since the result is indeterminate, you need to force `x^(3/2) ` factors at numerator and denominator:

`lim_(x->oo) (x^(3/2))(5/(x^(3/2)) - 2)/(x^(3/2)(3 - 4/x))`

Since `lim_(x->oo) 5/(x^(3/2)) = 0` and` lim_(x->oo)4/x = 0,` yields:

`lim_(x->oo) (x^(3/2 - 3/2))(-2/3) = -2/3*lim_(x->oo) (x^0) = -2/3*1 = -2/3`

Hence, evaluating the given limit yields `lim_(x->oo)(5 - 2x^(3/2))/(3x^(3/2) -4) = -2/3.`