`y = xsqrt(1 - x^2)` 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) x(sqrt(1-x^2))= (oo)(sqrt(1-oo))`

Since the result is indeterminate, you need to multiply and divide by `sqrt(1-x^2)` :

`lim_(x->-oo) (x(1-x^2))/(sqrt(1-x^2)) = oo/oo`

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

Since `lim_(x->-oo) 1/x^2 = 0` , yields:

`lim_(x->-oo) -x^2/(sqrt(1/x^2 - 1)) `

Since `sqrt -1 !in R` yields that `lim_(x->oo) x(sqrt(1-x^2))` cannot be evaluated.