Answer
The limit is equal to 105
Work Step by Step
$\lim\limits_{x \to 3}$ $5x^{3}$ - $3x^{2}$ + x -6
We use the fact that the limit of a sum is a sum of limits and the fact that the limit of a difference is the difference of limits to expand this expression to:
(1 )$\lim\limits_{x \to 3}$ $5x^{3}$ - $\lim\limits_{x_ \to 3}$ $3x^{2}$ + $\lim\limits_{x_ \to 3}$ x - $\lim\limits_{x_ \to 3}$ 6
We can now evaluate this limit term by term. Using the Direct Substitution Property we can plug in 3 for all values of x in expression (1).
=$5(3)^{3} - 3(3)^{2} + 3 - 6$
=135 - 27 + 3 - 6 = 105
