Question

Find the following limit or state that it does not exist. x² -81 lim X-9 X-9 Simplify the given limit. x² -81 lim X-9 = lim X-9 (Simplify your answer.) Evaluate the limit, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. lim -81 X-9 (Type an exact answer.) OB. The limit does not exist.

Answer 1

To find the limit of the given expression, factor the numerator and simplify. Substituting the value of x into the expression gives the final limit.

Step-by-step explanation:

To find the limit of the given expression, we can simplify it by factoring the numerator as the difference of squares. x² - 81 can be written as (x + 9)(x - 9). Now, cancel out the common factor of (x - 9) in the numerator and denominator. The limit becomes lim as x approaches 9 of (x + 9).

Substituting x = 9 into the expression, we get 9 + 9 = 18. Therefore, the limit of the given expression as x approaches 9 is 18.