Estimate the Limit by Graphing the Function for an Appropriate

Essay

Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-Find the error in the following incorrect application of L'Hôpital's Rule. $\lim _ { x \rightarrow 2 } \frac { x ^ { 3 } - 2 x ^ { 2 } + 1 } { 3 x ^ { 2 } - 6 x } = \lim _ { x \rightarrow 2 } \frac { 3 x ^ { 2 } - 4 x } { 6 x - 6 } = \lim _ { x \rightarrow 2 } \frac { 6 x - 4 } { 6 } = \frac { - 16 } { 6 }$ .