Question

find the limit.
lim(x→2) √(x² + 2x + 1)
±3
3
9
does not exist

Explanation:

Step1: Simplify the expression inside square - root

First, factor \(x^{2}+2x + 1=(x + 1)^{2}\). So, \(\lim_{x
ightarrow2}\sqrt{x^{2}+2x + 1}=\lim_{x
ightarrow2}\sqrt{(x + 1)^{2}}\).

Step2: Evaluate the limit

When \(x
ightarrow2\), we substitute \(x = 2\) into \(\sqrt{(x + 1)^{2}}\). Since \(\sqrt{(x + 1)^{2}}=\vert x + 1\vert\), when \(x=2\), \(\vert2 + 1\vert=3\).

Answer:

B. 3