\(\underset{x\rightarrow -\infty }{lim}\frac{\sqrt{4x^2-3x+1}}{2x+7} \\ =\underset{x\rightarrow -\infty }{lim}\frac{|x|\sqrt{4-3.\frac{1}{x}+\frac{1}{x^2}}}{x(2+\frac{7}{x})} \\ =\underset{x\rightarrow -\infty }{lim}\frac{-x\sqrt{4-3.\frac{1}{x}+\frac{1}{x^2}}}{x(2+\frac{7}{x})} \\ =\underset{x\rightarrow -\infty }{lim}\frac{-\sqrt{4-3.\frac{1}{x}+\frac{1}{x^2}}}{2+\frac{7}{x}} \\ =\frac{-\sqrt{4}}{2}=-1\)
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