The Limit of (x+6/x+1)^x+4 as x-->infinite

Solution:

$\\ L=\lim_{x\to\infty }(x+6/x+1)^x+4$ Form$\\ 1^\infty$

NOW,

$\\ \log L=\lim_{x\to\infty }(x+6/x+1 -1)\times x+4\\ \\\Rightarrow \log L=\lim_{x\to\infty }(5/x+1)\times (x+4)\\ \\\Rightarrow \log L=5\\ \\\Rightarrow L=e^5$

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