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

Textbook Question

Chapter 3, 3.5 - Problem 17a - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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

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

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

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

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

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

Hence, evaluating the given limit yields `lim_(x->oo) (5 - 2x^(3/2))/(3x^2 - 4) = 0.`

We’ve answered 318,983 questions. We can answer yours, too.

Ask a question