Answer
$1$
Work Step by Step
$\lim _{x\rightarrow \pi }\dfrac {\cos ^{2}x+3\cos x+2}{\cos x+1}=\dfrac {\left( \cos x+1\right) \left( \cos x+2\right) }{\cos x+1}=\cos x+2=\cos \pi +2=-1+2=1$
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