Step-by-step Solution

Find the limit $\lim_{x\to\infty }\left(x^{\frac{1}{x}}\right)$

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Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty}x^{\frac{1}{x}}$

Solving method

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(e^{\frac{1}{x}\ln\left(x\right)}\right)$

Unlock this full step-by-step solution!

Learn how to solve limits to infinity problems step by step online. Find the limit (x)->(\infty)lim(x^(1/x)). 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

$1$
$\lim_{x\to\infty}x^{\frac{1}{x}}$

Main topic:

Limits to Infinity

Related Formulas:

3. See formulas

Time to solve it:

~ 0.04 s