A) \[\frac{b}{a}\]
B) \[0\]
C) \[1\]
D) \[\frac{4}{5}\]
Correct Answer: C
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2}}+bx+4}{{{x}^{2}}+ax+5}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\left( 1+\frac{b}{x}+\frac{4}{{{x}^{2}}} \right){{x}^{2}}}{\left( 1+\frac{a}{x}+\frac{5}{{{x}^{2}}} \right){{x}^{2}}}\] Alternative\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2}}+bx+4}{{{x}^{2}}+ax+5}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2x+b}{2x+a}\](using\[L'\]Hospital?s rule) \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2}{2}\] \[=1\]
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