Question

$\huge \displaystyle\sf\lim\limits_{x\to\infty}\sqrt[x]{\dfrac{x!}{x^{x}}}$Or$\displaystyle\sf\lim\limits_{x\to\infty}\left(\dfrac{x!}{x}\right)^{\left(\dfrac{1}{x}\right)}$​​​

Answer 1

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What is Displaystyle?

\displaystyle command is used to over-ride automatic style rules and force display style; stays in force until the end of math mode or the braced group, or until another style is selected.