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limit n-infinity (4^n + 5^n)^1/n.

limit n-infinity (4^n + 5^n)^1/n.

Grade:12

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
\\ \\\lim _{x\to \infty \:}\left(\left(4^x+5^x\right)^{\frac{1}{x}}\right) \\=\lim _{x\to \infty \:}\left(e^{\frac{1}{x}\ln \left(4^x+5^x\right)}\right) \\=\lim _{x\to \infty \:}\left(e^{\frac{\ln \left(4^x+5^x\right)}{x}}\right) \\=e^{\ln \left(5\right)} \\=5 \\
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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