Find $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + x - 6 } { x - 2 }$
A) 2
B) -5
C) 5
D) DNE

Name: Find $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + x - 6 } { x - 2 }$ A) 2 B) -5 C) 5 D) DNE
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Question

Quizplus · Accepted Answer

The limit can be found by factoring the numerator and then simplifying. Factoring $x^2 + x - 6$ gives $(x + 3)(x - 2)$. The expression becomes $\frac{(x + 3)(x - 2)}{x - 2}$. Canceling $x - 2$ from the numerator and denominator, we are left with $x + 3$. Substituting $x = 2$ gives $2 + 3 = 5$.

Find lim⁡x→2x2+x−6x−2\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + x - 6 } { x - 2 }limx→2​x−2x2+x−6​

Find $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + x - 6 } { x - 2 }$