Question

Evaluate the following limit. enter an exact answer. limx→−9x2−81x 9=

Answer 1

To evaluate the limit, substitute -9 for x, then apply L'Hopital's rule to differentiate the numerator and denominator separately. The exact value of the limit is -18.

Step-by-step explanation:

To evaluate the limit
`lim(x\rightarrow -9) (x^2-81)/(x+9)`, we can substitute -9 for x in the expression first.

So we have
`(-9)^2-81/(-9+9)` = 0/0.

Since we get 0/0, we can apply L'Hopital's rule to differentiate the numerator and denominator separately.

After differentiating, we have 2x/1 = 2(-9)/1

= -18/1

= -18

Therefore, the exact value of the limit is -18.