A) \[{{e}^{12}}\]
B) \[{{e}^{-12}}\]
C) \[{{e}^{4}}\]
D) \[{{e}^{3}}\]
Correct Answer: B
Solution :
Given that, \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{4}{x-1} \right)}^{3x-1}}\] \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left[ {{\left( 1-\frac{4}{x-1} \right)}^{\frac{-(x-1)}{4}}}\,\,\,\,\,\, \right]}^{4\left( \frac{3x-1}{x-1} \right)}}\] \[\Rightarrow \,\,{{e}^{-4\,\,\underset{x\to \infty }{\mathop{\lim }}\,\,\,(3-1/x)/(1-1/x)}}\] \[\Rightarrow \,\,{{e}^{-4\,\,\times 3}}\] \[\Rightarrow {{e}^{-12}}\]
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