Final Answer
$1$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to\infty }\left(x^{\frac{1}{x}}\right)$
Specify the solving method
1
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
$\lim_{x\to\infty }\left(e^{\frac{1}{x}\ln\left(x\right)}\right)$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(e^{\frac{1}{x}\ln\left(x\right)}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of x^(1/x) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(x\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.
Final Answer
$1$
Exact Numeric Answer
$1$