Find the limit of the function algebraically.
-$$\lim _ { x \rightarrow 6 } \frac { x + 6 } { ( x - 6 ) ^ { 2 } }$$
A) 0
B) $- 6$
C) 6
D) Does not exist

Question

Quizplus · Accepted Answer

The denominator of the fraction $(x - 6)^2$ approaches 0 as $x$ approaches 6, while the numerator approaches 12. This results in a form that suggests the limit will approach infinity or negative infinity, depending on the direction from which $x$ approaches 6. Since the denominator is squared, it will always be positive, leading to a positive infinity outcome. However, because the question is about the existence of a limit in a general sense, when a function approaches infinity as $x$ approaches a certain value, it is said that the limit does not exist in the real number system.

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

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