Math, asked by mayankgoyal7534, 2 months ago

plz give answer of this​

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Answered by Anonymous
49

Answer:

\large \pmb{\bf{\underline{\gray{Solution :-}}}}

 \sf {Assume\:\:\displaystyle \lim_{x\to\infty}\left ( \dfrac{x!}{x} \right )^{\dfrac{1}{x}} = L}

Take log both sides, we get

 \sf {ln(L)=\displaystyle \lim_{x\to\infty} \left ( \dfrac{1}{x} \right )ln \left ( \dfrac{x!}{x} \right )}

 \pmb{\sf{\gray{ Put\ value\ of\ x! }}}

 \sf {ln(L)=\displaystyle \lim_{x\to\infty} \left ( \dfrac{1}{x} \right )ln \left ( \dfrac{x(x-1)!}{x} \right )}

 \sf {ln(L)=\displaystyle \lim_{x\to\infty} \left ( \dfrac{1}{x} \right )ln \left ( (x-1)! \right )}

 \sf {ln(L)=\displaystyle \lim_{x\to\infty} \dfrac{ln \left ( (x-1)! \right )}{x}}

\pmb{\tt{Multiplying \ with\ ( x - 1 )\ in\ numerator\ and\ denominator\, we\ get\ }}

\sf {ln(L)=\displaystyle \lim_{x\to\infty} (x-1)\dfrac{ln \left ( (x-1)! \right )}{x(x-1)}}

 \pmb{\sf{We\ know\ that}}

 \sf {\displaystyle \lim_{x\to\infty} \dfrac{ln \left ( x! \right )}{x}=\infty}

 \sf {ln(L)=(\infty) \displaystyle \lim_{x\to\infty} \dfrac{x-1}{x}}

 \sf {ln(L)=(\infty) \displaystyle \lim_{x\to\infty} \left(1-\dfrac{1}{x}\right)}

Put value of limits,

 \sf {ln(L)=(\infty) \left(1-\dfrac{1}{\infty}\right)}

 \sf {ln(L)=(\infty) \left(1-0\right)}

 \sf {ln(L)=\infty}

 \sf{L=e^{\infty}}

 \sf{L=\infty}

Step-by-step explanation:

hopes its helps you..

Answered by LaRouge
3

Answer:

7,874,965,825

the population of

World Population

is

TOP 10 MOST POPULOUS COUNTRIES (July 1, 2021)

1. China 1,397,897,720 6. Nigeria 219,463,862

2. India 1,339,330,514 7. Brazil 213,445,417

3. United States 332,475,723 8. Bangladesh 164,098,818

4. Indonesia 275,122,131 9. Russia 142,320,790

5. Pakistan 238,181,034 10. Mexico 130,207,371

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