a > b:
\( \lim \limits_{x \to \infty} \sqrt[x]{a^x+ b^x} \) =
\( \lim \limits_{x \to \infty}\sqrt[x]{a^x ( 1 + (\frac{b}{a})^x)} \) =
\( \lim \limits_{x \to \infty}a* \sqrt[x]{1 + (\frac{b}{a})^x} \) = a
b > a:
\( \lim \limits_{x \to \infty} \sqrt[x]{a^x+ b^x} \) =
\( \lim \limits_{x \to \infty}\sqrt[x]{b^x ((\frac{a}{b})^x + 1)} \) =
\( \lim \limits_{x \to \infty}b* \sqrt[x]{(\frac{a}{b})^x + 1} \) = b
a = b:
\( \lim \limits_{x \to \infty} \sqrt[x]{2*a^x} \) =
\( \lim \limits_{x \to \infty} a*\sqrt[x]{2} \) = a = b