Find
$$\lim _ { x \rightarrow 7 } \frac { x - 8 } { x ^ { 2 } + 12 x + 27 }$$
by direct substitution.
A) $\frac { 1 } { 160 }$
B) $- \frac { 1 } { 160 }$
C) 0
D) $\infty$
E) limit does not exist

Question

Quizplus · Accepted Answer

Direct substitution of $x = 7$ into the given limit yields $\frac{7 - 8}{7^2 + 12(7) + 27} = \frac{-1}{49 + 84 + 27} = \frac{-1}{160}$.

Find lim⁡x→7x−8x2+12x+27\lim _ { x \rightarrow 7 } \frac { x - 8 } { x ^ { 2 } + 12 x + 27 }x→7lim​x2+12x+27x−8​

Find $\lim _ { x \rightarrow 7 } \frac { x - 8 } { x ^ { 2 } + 12 x + 27 }$