Question

find the limit.
lim (3x^3 - 2x^2 + 5x + 1)
x→1

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. lim (3x^3 - 2x^2 + 5x + 1) = (simplify your answer.)
x→1

b. the limit does not exist

Explanation:

Step1: Substitute x = 1

Substitute \(x = 1\) into \(3x^{3}-2x^{2}+5x + 1\).
\[3\times(1)^{3}-2\times(1)^{2}+5\times(1)+1\]

Step2: Calculate each term

Calculate each term: \(3\times(1)^{3}=3\), \(-2\times(1)^{2}=-2\), \(5\times(1) = 5\).
\[3-2 + 5+1\]

Step3: Simplify the expression

\[3-2+5 + 1=(3-2)+(5 + 1)=1 + 6=7\]

Answer:

A. \(\lim_{x
ightarrow1}(3x^{3}-2x^{2}+5x + 1)=7\)