find the limit.\nlim(x→2) √(x² + 2x + 1)\n±3\n3\n9\ndoes not exist

Explanation:

Step1: Simplify the expression inside square - root

First, factor (x^{2}+2x + 1=(x + 1)^{2}). So, (\lim_{x\rightarrow2}\sqrt{x^{2}+2x + 1}=\lim_{x\rightarrow2}\sqrt{(x + 1)^{2}}).

Step2: Evaluate the limit

When (x\rightarrow2), 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