A) \[-1/2\]
B) 0
C) \[1/2\]
D) 1
Correct Answer: A
Solution :
\[\underset{x\,\to \,-\infty }{\mathop{\lim }}\,\,\frac{\sqrt{4{{x}^{2}}+5x+8}}{4x+5}\]\[=\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{\sqrt{4\,{{(-1/h)}^{2}}+5\,(-1/h)+8}}{4\,(-1/h)+5}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{(1/h)\sqrt{4\,-5h+8{{h}^{2}}}}{(1/h)\,(-\,4+5h)}=\frac{\sqrt{4}}{-4}=-\frac{1}{2}\].
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