Find the limit of the function algebraically.
-$$\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } - 36 } { x + 6 }$$
A) $- 6$
B) $- 12$
C) Does not exist
D) 1

Question

Quizplus · Accepted Answer

The function can be simplified by factoring the numerator as $\frac{(x+6)(x-6)}{x+6}$, which simplifies to $x-6$ when $x \neq -6$. Substituting $x = 6$ gives $6 - 6 = 0$, so the correct answer is $-12$, not $0$. My previous explanation contained an error in the final calculation. The correct calculation after simplification and substituting $x = 6$ should indeed result in $6 - 6 = 0$, but the process described was intended to find the limit as $x$ approaches $6$, not the value after simplification. The correct approach is to factor and simplify the expression to $x - 6$ and then substitute $x = 6$, which actually results in $0$, not $-12$. Therefore, the explanation mistakenly claimed the answer was $-12$ due to a miscalculation. The correct process leads to the limit being $6 - 6 = 0$, which indicates an error in the provided options and explanation.

Find the Limit of the Function Algebraically lim⁡x→6x2−36x+6\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } - 36 } { x + 6 }x→6lim​x+6x2−36​

Find the Limit of the Function Algebraically $\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } - 36 } { x + 6 }$