A) 5
B) 3
C) 1
D) 0
Correct Answer: D
Solution :
[d] \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{5}^{n+1}}+{{3}^{n}}-{{2}^{2n}}}{{{5}^{n}}+{{2}^{n}}+{{3}^{2n+3}}}=\underset{n\,\to \,\infty }{\mathop{\lim }}\,\frac{{{5.5}^{n}}+{{3}^{n}}-{{4}^{n}}}{{{5}^{n}}+{{2}^{n}}+{{27.9}^{n}}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\frac{5.\frac{{{5}^{n}}}{{{9}^{n}}}+\frac{{{3}^{n}}}{{{9}^{n}}}-\frac{{{4}^{n}}}{{{9}^{n}}}}{\frac{{{5}^{n}}}{{{9}^{n}}}+\frac{{{2}^{n}}}{{{9}^{n}}}+27}=\frac{0+0-0}{0+0+27}=0.\]
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