Answer:

Step-by-step explanation:
The image below shows step-by-step on how to solve it.
<em>Hope this helps! </em>:)
Answer:
We want to find:
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D)
Here we can use Stirling's approximation, which says that for large values of n, we get:

Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7B%5Csqrt%7B2%2A%5Cpi%2An%7D%20%2A%28%5Cfrac%7Bn%7D%7Be%7D%20%29%5En%7D%20%7D%7Bn%7D%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bn%7D%7Be%2An%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D)
Now we can just simplify this, so we get:
![\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Be%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D%20%5C%5C)
And we can rewrite it as:

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:

Depend on the comparison. if u want to see greater or less then use = < > or the difrent subtract . add if finding the total.
Answer:
that is 6 and 5/ 12 cups of flour are required
Step-by-step explanation:
total number of cups required to make a loaf of bread
= 3 + ¾
making their denominators equal and that to 4
= 12/ 4 + 3/ 4
adding numerators
= (12 + 3)/ 4
= 15/ 4
total cups of flour required to make pretzels
= 2 + ⅔
making their denominators equal and that to 3
= 6/ 3 + 2/ 3
adding nunerators
= (6 + 2)/ 3
= 8/ 3
Total cups required:-
= 15/ 4 + 8/ 3
taking lcm of denominators to make the fractions equivalent
= {(15 × 3) + (8 × 4)}/ 12
= {45 + 32}/ 12
= 77/ 12

<em>that is 6 and 5/ 12 cups of flour are required</em>.
Answer:
a
Step-by-step explanation: