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

Textbook Question

Chapter 3, 3.9 - Problem 17 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`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's profile pic

scisser | (Level 3) Honors

Posted on

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.

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