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Math  /  Calculus

QuestionFind the limit. lim⁡x→−9x2+5x−36x+9\lim _{x \rightarrow-9} \frac{x^{2}+5 x-36}{x+9}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim⁡x→−9x2+5x−36x+9=5\lim _{x \rightarrow-9} \frac{x^{2}+5 x-36}{x+9}=5 (Type an integer or a simplified fraction.) B. The limit does not exist.

Studdy Solution
Evaluate the limit by direct substitution.
lim⁡x→−9(x−4)=−9−4=−13 \lim _{x \rightarrow -9} (x - 4) = -9 - 4 = -13
Therefore, the limit is:
lim⁡x→−9x2+5x−36x+9=−13 \lim _{x \rightarrow -9} \frac{x^{2}+5 x-36}{x+9} = -13
The correct choice is:
A. lim⁡x→−9x2+5x−36x+9=−13 \lim _{x \rightarrow -9} \frac{x^{2}+5 x-36}{x+9} = -13

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