A) 4
B) 3
C) e
D) \[\infty \]
Correct Answer: A
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,{{({{3}^{n}}+{{4}^{n}})}^{1/n}}\] \[\underset{n\to \infty }{\mathop{\lim }}\,{{\left[ {{4}^{n}}\left( \frac{{{3}^{n}}}{{{4}^{n}}}+1 \right) \right]}^{1/n}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,4{{\left[ {{\left( \frac{3}{4} \right)}^{n}}+1 \right]}^{1/n}}\] \[=4\,(0+1)\,\,\,\left[ \because \underset{n\to \infty }{\mathop{\lim }}\,\,\,{{r}^{n}}\to 0\,if\,r<1 \right]\] = 4
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