![\displaystyle\sf\lim\limits_{x\to\infty}\sqrt[x]{\dfrac{x!}{x^{x}}} \displaystyle\sf\lim\limits_{x\to\infty}\sqrt[x]{\dfrac{x!}{x^{x}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csf%5Clim%5Climits_%7Bx%5Cto%5Cinfty%7D%5Csqrt%5Bx%5D%7B%5Cdfrac%7Bx%21%7D%7Bx%5E%7Bx%7D%7D%7D)
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Answers
Answered by
77
Topic :-
Limits
To Solve :-
Solution :-
Take log both sides,
x! = x( x - 1 )( x - 2 ). . . . . . . 3 × 2 × 1
x! = x( x - 1 )!
Put value of x!,
Multiplying with ( x - 1 ) in numerator and denominator,
We know that,
Put value of limits,
Answer :-
So, value of the limit 'L' is .
Answered by
25
Answer:
★᭄ꦿ᭄Answer★᭄ꦿ᭄
Take log both sides, we get
Put value of limits,
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