Find $\lim _ { t \rightarrow 6 } \frac { t ^ { 3 } - 216 } { t - 6 }$ .
A)18
B)72
C)108
D)6
E)limit does not exist

Question

Quizplus · Accepted Answer

The limit can be solved by factoring the numerator as a difference of cubes: $t^3 - 216 = (t - 6)(t^2 + 6t + 36)$. The denominator $t - 6$ cancels out, leaving $\lim _ { t \rightarrow 6 } (t^2 + 6t + 36)$. Substituting $t = 6$ gives $6^2 + 6(6) + 36 = 36 + 36 + 36 = 108$.

Find lim⁡t→6t3−216t−6\lim _ { t \rightarrow 6 } \frac { t ^ { 3 } - 216 } { t - 6 }limt→6​t−6t3−216​

Find $\lim _ { t \rightarrow 6 } \frac { t ^ { 3 } - 216 } { t - 6 }$