Use the TABLE feature of a graphing utility to find the limit.
-$\lim _ { d \rightarrow } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)$
A) 27
B) 9
C) 0
D) does not exist

Question

Quizplus · Accepted Answer

The given limit can be simplified by factoring the numerator as $(d-3)(d^2+3d+9)$ and then canceling out the $(d-3)$ term, which gives $\lim _ { d \rightarrow 3 } \left( d^2 + 3d + 9 \right)$. Substituting $d = 3$ into this expression yields $3^2 + 3(3) + 9 = 9 + 9 + 9 = 27$. However, since the original question is asking for the limit as $d$ approaches 3, not the value after substitution into the simplified expression, the correct interpretation involves evaluating the derivative at the point of interest due to the cancellation. The derivative approach (or recognizing the factoring mistake in the explanation) leads to the correct limit value as $d$ approaches 3, which is $27$, but the explanation provided was incorrect in its final evaluation. The correct process involves recognizing that after simplification, the limit evaluates directly to the expression at $d = 3$, which indeed gives $27$, not $9$. The mistake was in the explanation of the simplification and evaluation process. The correct answer, based on the proper calculation, should be evaluated by recognizing the direct substitution possibility after simplification, which indeed yields $27$, not $9$, as incorrectly concluded in the explanation.

Use the TABLE Feature of a Graphing Utility to Find lim⁡d→(d3−27d−3)\lim _ { d \rightarrow } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)limd→​(d−3d3−27​)

Use the TABLE Feature of a Graphing Utility to Find $\lim _ { d \rightarrow } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)$