Question

find the limit.
lim (3x³ - 3x² + 2x + 3)
x→1
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. lim (3x³ - 3x² + 2x + 3) = (simplify your answer.)
x→1
b. the limit does not exist.

Explanation:

Step1: Substitute \(x = 1\) into the polynomial

We use the direct - substitution property for polynomials. For a polynomial \(P(x)=3x^{3}-3x^{2}+2x + 3\), the limit as \(x
ightarrow a\) is \(P(a)\).
Substitute \(x = 1\) into \(P(x)=3x^{3}-3x^{2}+2x + 3\):

$$
LATEXBLOCK0
$$

Step2: Simplify the expression

$$
LATEXBLOCK1
$$

Answer:

A. \(\lim_{x
ightarrow1}(3x^{3}-3x^{2}+2x + 3)=5\)