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:
Answer:
The coordinates of P' are (4.8,-4.8).
Step-by-step explanation:
The rule of dilation 
represent the dilation with scale factor 2.4 and center at origin.
If the scale factor of the dilation is k and the center is (0,0), then
Since the scale factor is 2.4, therefore
From the given figure it is noticed that the coordinates of P are (2,-2). The coordinates of P' are
Therefore the coordinates of P' are (4.8,-4.8).
Answer:
2
b
+
9
m
+
6
x
+
10
Step-by-step explanation:
2
b
+
4
+
6
x
+
6
+9
m
2
b
+
6
x
+
10
+
9m
2
b
+
6
x
+
9
m
+
10
= 2
b
+
9
m
+
6
x
+
10
The bar should be 8 1/24 from the each edge of the door.
We need to subtract 10 1/4 from 26 1/3 to get the fraction of the space not covered by the towel bar.
We also need to divide the difference by 2 because we placed the towel bar in the center of the door.
1st we need to convert the mixed fractions into fractions to perform subtraction.
26 1/3 = ((26*3)+1)/3 = 79/3
10 1/4 = ((10*4)+1)/4 = 41/4
Steps in Subtracting Fractions
Step 1. Make sure the denominator is the same. 3 and 4 are the denominators, they are not the same but they are factor of 12. So,
79/3 must be multiplied by 4 = 79 * 4 / 3 * 4 = 316 / 12
41/4 must be multiplied by 3 = 41 * 3 / 4 * 3 = 123 / 12
Step 2. Subtract the numerators and place them above the common denominator
316/12 - 123/12 = 316 - 123 / 12 = 193 / 12
Before we can simplify the fraction, we must divide it by two to get the measurement of each edge of the door.
Steps in dividing fractions.
Step 1. Get the reciprocal of the 2nd fraction.
1st fraction : 193 / 12
2nd fraction : 2 /1 ⇒ reciprocal 1/2
Step 2. Multiply the 1st fraction to the reciprocal of the 2nd fraction
193 / 12 * 1/2 = 193 * 1 / 12 * 2 = 193 / 24
Step 3. Simplify the fraction.
193 / 24 = 8 1/24
Answer: 48
Step-by-step explanation: if i did the math correct 1/3 times the base (9) times 16 is 48. the formula is 1/3 x Bh
