find the limit. use lhospitals rule where appropriate. if there is a more elementary method, consider using…

find the limit. use lhospitals rule where appropriate. if there is a more elementary method, consider using it. \n lim _{x \rightarrow 9} \frac{x^{2}-7 x-18}{x-9}

find the limit. use lhospitals rule where appropriate. if there is a more elementary method, consider using it. \n lim _{x \rightarrow 9} \frac{x^{2}-7 x-18}{x-9}

Answer

Explanation:

Step1: Factor the numerator

The numerator (x^{2}-7x - 18) can be factored as ((x - 9)(x+2)). So the limit becomes (\lim_{x\rightarrow9}\frac{(x - 9)(x + 2)}{x - 9}).

Step2: Simplify the function

Cancel out the common factor ((x - 9)) (for (x\neq9)). The simplified function is (y=x + 2).

Step3: Evaluate the limit

Substitute (x = 9) into (y=x + 2). We get (y=9+2).

Answer:

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