A) \[{{e}^{4}}\]
B) \[{{e}^{3}}\]
C) \[{{e}^{2}}\]
D) e
Correct Answer: A
Solution :
[a] : \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+3} \right)}^{x}}({{1}^{\infty }}form)\] \[=\exp \left\{ \underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+3}-1 \right)x \right\}\] \[=\exp \left\{ \underset{x\to \infty }{\mathop{\lim }}\,\frac{4{{x}^{2}}}{{{x}^{2}}+x+3} \right\}={{e}^{4}}\]
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