`y = sqrt(9 - x^2)` Find the limit, if possible

Expert Answers
gsarora17 eNotes educator| Certified Educator

`lim_(x->0)sqrt(9-x^2)`

plug in the value of x to evaluate the limit

= `sqrt(9-0^2)=3`

`lim_(x->oo)sqrt(9-x^2)`

=`sqrt(9-oo^2)`

limit does not exist

scisser | Student

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

`lim_(x->oo)sqrt(9-(oo)^2) `

Since ` ` you are subtracting a really, really big number from 9, the result on the inside of the square root will be negative. It is not possible to take the square root of a negative number (unless we involve the imaginary `i ` ).

Therefore,

the `lim_(x->oo)sqrt(9-x^2) ` does not exist.