courtr51
Answered

Find the limit of the function algebraically.


limit as x approaches negative six of quantity x squared minus thirty six divided by quantity x plus six.

Verified Answer :

nobillionaireNobley

\(lim_{x \rightarrow -6} \frac{x^2-36}{x+6} \\ =lim_{x \rightarrow -6} \frac{(x-6)(x+6)}{x+6} \\ =lim_{x \rightarrow -6} (x-6) \\ =-6-6=-12\)

Answer:

-12

Step-by-step explanation:

\(\lim_{x \to \ -6} \frac{x^2-36}{x+6}\)

We factor the numerator and try to simplify the fraction as much as we can.

\(x^2-36 = x^2 - 6^2\)

Apply a^2 - b^2 formula (a+b)(a-b)

\(x^2-36 = x^2 - 6^2=(x+6)(x-6)\)

\(\lim_{x \to \ -6} \frac{(x+6)(x-6}{x+6}\)

Cancel out x+6 from top and bottom

\(\lim_{x \to \ -6}(x-6)\)

Plug in -6 for x

-6-6 = -12

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