Answers
Answer:
We want to find:
[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]
Here we can use Stirling's approximation, which says that for large values of n, we get:
[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
[tex]\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}[/tex]
Now we can just simplify this, so we get:
[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]
And we can rewrite it as:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]
Related Questions
Write a polynomial that represents the area of the above football field.
Answers
Answer:
36x² + 24x + 300 ft²
Step-by-step explanation:
→ Area of rectangle = Length × Width
→ Area of rectangle = (12x + 8) ft × (3x + 15) ft
→ Area of rectangle = 12x(3x + 15) + 8(3x + 15) ft²
→ Area of rectangle = 36x² + 180 + 24x + 120 ft²
→ Area of rectangle = 36x² + 24x + 300 ft²
Find the missing segment in the image below
Answers
A researcher wants to calculate the average variability from the mean of the scores in their normally-distributed data set. For each participant, they calculate a deviation score. The researcher then sums all the deviation scores together and is surprised to find that the average deviation from the mean in the group is zero. Which of the statements below is FALSE about this scenario?
A. Deviation scores can be used to calculate sum of squares, variability, and then standard deviation.
B. Approximately the deviation scores will be positive and half will be negative.
C. Deviation scores are calculated by subtracting the participant score from the mean.
D. Average deviation from the mean in the group must be squared to be meaningful.
Answers
Answer:
D. Average deviation from the mean in the group must be squared to be meaningful.
Step-by-step explanation:
The average variability from mean is not calculated with mean square of the selected group. The deviation scores calculated by subtracting participant score from the mean.
i don't know what to do so can someone help me
Answers
Answer:
1. 8r+7
2. 8 ( r-t)
3. 2(3r+5t)
Step-by-step explanation:
See Image below:)
1. = 8r+7t
2. = 8(r+t)
3. = 8(r-t)
I need help please no links or I will have you reported
Answers
Answer:ʜᴛᴛᴘꜱ://ᴡᴡᴡ.ʏᴏᴜᴛᴜʙᴇ.ᴄᴏᴍ/ᴡᴀᴛᴄʜ?ᴠ=ᴅQᴡ4ᴡ9ᴡɢxᴄQ
Step-by-step explanation:
Heres the answer but its on a another page.
Im joking
here's the answer
the first one is 878 i think that what your looking for at the top
PLEASE ANSWER ASAP - I WILL MARK BRAINLIEST!!!!!!!!
Answers
Answer:
2/3
Step-by-step explanation:
P ( 8 or more) = number that are 8 or more) / total
= (6+4) / ( 2+3+6+4)
= 10/15
=2/3
2097152 in exponential form
Answers
Answer:
do you mean scientific notation ?
2.097152 x [tex]10^{6}[/tex]
Step-by-step explanation:
can anyone help for me in this questions
Answers
Answer:
Step-by-step explanation:
Note : any number or variable with it's power 0 is considered as one.
Last one is the solution to find the two ration numbers between 2/5 and 3/4 (question which u asked just before this question).
Question 11 of 40
Factor this polynomial completely.
x2 - 6x + 9
A. (x+3)(x+3)
B. Does not factor
C. (x-3)(x - 3)
D. (x+3)(x-3)
Answers
What is the reflection across y=x and y=-x. Just the general definition of what it means.
Answers
Answer: When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Reflection in the y -axis:
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Reflecting over any other line. Notice how each point of the original figure and its image are the same distance away from the line of reflection (x = –2 in this example).
It is simple enough to identify whether or not a given function f(x) is a linear transformation. Just look at each term of each component of f(x). If each of these terms is a number times one of the components of x, then f is a linear transformation. are linear transformations.
First shift three units to the left, so the line of reflection becomes the y axis, then flip, and finally remember to shift three units back to the right to put the center line back where it belongs. (This gives the f(6−x) solution you already know).
More information for you..
https://youtu.be/TPU5IyCUGuA
https://youtu.be/JHQtA6R7fYc
https://youtu.be/LR6f23gY3qk
[tex]\color{yellow}{}[/tex]
Dennis collected a total of 1712 stamps over the past 16 years At this rate how many stamps would he collect in 21 years
Answers
2,247
Step-by-step explanation:
you take 1712 and divide that by 16 which is 107 and then you multiply 107 by 21 thus you get 2,247.
PLZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Task #2 EZ Coasters
Emma and Zeke own an on-line business, EZ Coasters, that sells cork beverage coasters, which can be bought plain or with logos. The price for both types of coasters is $3.00 each. There is also a one-time set-up charge of $25 for coasters with a logo.
1) Write an equation describing the relationship between:
a) The number of plain coasters bought and the cost of the coasters.
b) The number of coasters with a logo bought and the price of the coasters.
c) Is either coaster relationship proportional? Explain in writing how you know.
d) Explain what the unit rate of the line described by each equation means in the context of the coasters.
2) EZ Sales also sells plain natural sandstone coasters for $4.00 each.
a) Write the equation describing this relationship.
b) Indicate whether or not it is a proportional relationship and explain why?
c) Will the graph of this equation ever intersect the graph of the equations for either of the other two EZ Coasters? Explain in typing how you made your decision.
Answers
Answer:
7
Step-by-step explanation:
3^4 +3 • 5= _. (Input whole numbers only.) Numerical Answers Expected! Please explain.
Answers
Answer:
96
Step-by-step explanation:
81+15=96
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{3^4 +3 \times5}\\\\\\\mathsf{3^4}\\\mathsf{= 3\times3\times3\times3}\\\mathsf{=9\times9}\\\mathsf{= \bf 81}\\\\\\\mathsf{81+5\times3}\\\\\mathsf{3\times5=\bf 15}\\\\\\\\\mathsf{81+15}\\\mathsf{= \bf 96}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 96}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A grande with a counter weight is shown in the figure. Find the horizontal distance between points A and D.
Answers
Step-by-step explanation:
the answer is in the above image
In a math class, 9 pupils receive a grade of 90. If 18% of the class got 90, how many pupils are there in a class?
Answers
Answer:
Let the total number of pupil be x.
Given that,
Number of pupils that received a grade of 90=9
Percentage of pupil that receive a grade of 90=18%
So,
18% of x=9
18x/100=9
x=50
Hence, there are 50 pupils in the class.
Experience shows that few students hand in their statistics exams early; most prefer to hand them in near the end of the test period. This means the time taken by students to write exams is positively skewed.
a. True
b. False
Answers
Answer:
False
Step-by-step explanation: 6 28 13 50
skewing to the right of a sysmetrical distribution is a negative skew
What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices
Answers
Answer:
Answer is C
Step-by-step explanation:
In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down
In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up
Demand Schedule is a Chart
Demand Curve is a graph
Supply Schedule is a Chart
Supply Curve is a graph
Hope this helps
Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
Which best describes the range of the function f(x) = 2(3)x?
Answers
Answer:
y > 0.
Step-by-step explanation:
A.
7.5 7 2/5 7.69 in order
Answers
Answer:
ok for this problem lets convert all of the number into decimals to make it easier.
7.5 is already a decimal
7 2/5 as a decimal is 7.4
7.69() is already a decimal
ok so 7.4 is lowest
7.5 is next
7.69 is highest
Answer:
In order from least to greatest is [tex]7\frac{2}{5},7.5,7.69[/tex]
Step-by-step explanation:
In order from greatest to least is the other way around
[tex]2/5 = 0.4[/tex]
So [tex]7.4[/tex]
Hope this is helpful
3 Connor is painting a superhero with this belt buckle shown. What is the area of the belt buckle in square Inches? 9 inches 2.5 inches 4 inches 5 inches 15 inches 2.5 mches The area in square Inches is:
HELP PLSSS
Answers
Answer:
87.5 square inches
Step-by-step explanation:
(For Diagram,Please Find in Attachment)
Given, in diagram of the belt Knuckle there are 4 Triangles (2 are of same dimensions & another 2 are of same dimensions) and a Rectangle .
Now For Area of belt Knucle, We have to First Calculate the area of 4 triangles and Area of Rectangle.
∴ Area of 2 Triangle with given dimensions ( height = 2.5 inches & base = 9 inches )
Area = 2×(1/2×b×h) ⇔ 2×(1/2×9×2.5)
Area= 22.5 square inches
∴ Area of another 2 triangle with given dimensions ( height = 5 inches & base = 4 inches )
Area = 2×(1/2×b×h) ⇔ 2×(1/2×4×5)
Area= 20 square inches
∴Area of Rectangle with given dimensions ( Length = 9 inches & Width = 5 inches )
Area= length × Width ⇔ 9×5 ⇒ 45 square inches
Now, Area of belt Knucle=Sum of Area of 4 Triangles + Area of Rectangle
Area of belt Knucle = 87.5 square inches
Given f(x)=10-2x, find f(7)
Answers
Answer:
-4
Step-by-step explanation:
f(x) = 10 - 2x
substitute 7 in place of x
f(7) = 10 -2*7
=10 - 14
=-4
therefore the value of f(7) is -4.
Write equation could use to find number of centimeters in 1 inch.
Answers
Answer:
0.393701 cm = 1 in
Step-by-step explanation:
We want to find the number of centimeters in 1 inch.
First, the two conversion rates we need to use:
1m = 100 cm
1m = 39.3701 in
From these two equations, we can conclude that:
100cm = 1m = 39.3701 in
100cm = 39.3701 in
Because we want to find the total number of centimeters in 1 inch, we need to divide both sides by 39.3701
We will get:
(100cm)/39.3701 = (39.3701 in)/39.3701
0.393701 cm = 1 in
This equation gives us the number of centimeters in one inch.
23.
Rewrite the equation of the circle (x + 2)2 + (y + 5)2 = 9 in general form.
A. x2 + y2 + 4x + 5y +20 = 0
B. x2 + y2 + 4x+10y+38 = 0
C. x2 + y2 +4x+10y+20 = 0
D. x2 + y2 +2x+10y+20= 0
Answers
Answer:
The answer is C .
Step-by-step explanation:
Here's your answer in image
Answer:
The answer is C
Step-by-step explanation:
Your Answer is in the above image
please help me...........
Answers
I will help u if I know in cmt
can someone answer this please
Answers
Answer:
ArcAB should be 182.
Step-by-step explanation:
You are not going to believe this, because the diagram is very misleading. AC is the same as the central angle. The central angle is twice m<ABC.
The central angle = 2*91 = 182
Please help me with math problems!
20 points for all questions plz
Answers
Answer:
Step-by-step explanation:
[tex]Circumference = 2 \pi r[/tex]
1) r = 11 feet
Circumference = 69.1 ft
2) r = 7yd
Circumference = 43.98 = 44 yd
3) r = 6.3 m
Circumference = 39.6
4) r = 11.8 ft
Circumference = 74. 1 ft
5) r = 2 km
Circumference = 12.6 km
6) r = 9 mi
Circumference = 56.6 mi
7) r = 6 ft
Circumference = 37. 7ft
8) r = 8. 4 ft
Circumference = 52.8 ft
[tex]Circumference = 2 \pi r = \pi \times 2r = \pi \times d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ diameter, d = 2r \ ][/tex]
11) d = 4m
Circumference = 12.6 m
12) d = 22 mi
Circumference = 69.1 mi
13) d = 5m
Circumference = 15.7 m
14) d = 8yd
Circumference = 25.1 yd
15) d = 16.8 m
Circumference = 52.8 m
16) d = 6cm
Circumference = 18.9 cm
17) d = 14 in
Circumference = 43.98 = 44 in
18) d = 16km
Circumference = 50. 3 km
Answer:
1) 69.1
2) 44
3) 39.6
4) 74.1
5) 12.6
6) 56.5
7) 37.7
8) 52.8
11) 12.6
12) 69.1
13) 15.7
14) 25.1
15) 52.8
16) 18.8
17) 44
18) 50.3
This was a lot but I'm pretty sure all are right
Simplify -4 + (-3) + 6.
Answers
Answer:3/6 in simplest fraction form is 1/2.
Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out
Solve the equation on the interval (0,2pi). Write your answer in exact simplest form.
[tex]cos6x-5sin3x+2=0[/tex]
Answers
9514 1404 393
Answer:
x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}
Step-by-step explanation:
Using the trig identity ...
cos(2x) = 1 -2sin²(x)
we can rewrite the equation as ...
(1 -2sin²(3x)) -5sin(3x) +2 = 0
2sin²(3x) +5sin(3x) -3 = 0 . . . . . standard form
(sin(3x) +3)(2sin(3x) -1) = 0 . . . . factored form
There are no real values of x that will make the first factor zero. The second factor is zero when ...
sin(3x) = 1/2
3x = arcsin(1/2) +2nπ or (2n+1)π -arcsin(1/2)
x = 1/3(π/6 +2nπ) or 1/3((2n +1)π -π/6)
x = (12n+1)π/18 or (12n+5)π/18
x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}
Which of the following is most likely next in the series?
Answers
Answer:
B.
Step-by-step explanation:
Judging by the picture, it appears that you are correct. The pattern seems to go as follows:
1. Blue (with one line)
2. Red (with two lines)
3. Blue (with three lines)
This means that your final step should be red with four lines, and we can eliminate D as there is no sign that the line should branch off that way (based on the pattern that we already have). Hope this helps and please let me know if you still need help!
The slope f '(x) at each point (x, y) on a curve. y = f (x) is given along with a particular point (a, b) on the curve. Use this information to find f (x).
[CLO-3] f '(x) = 9 x 2 + 4 x - 4; (0, -7)
Answers
Answer:
Step-by-step explanation:
Integrating each term with respect to x, we get:
x^3 x^2
f(x) = 9--------- + 4------- - 4x + C
3 2
We are told that if x = 0, f(x) = -7, and so C must equal - 7.
The solution is
x^3 x^2
f(x) = 9--------- + 4------- - 4x - 7, or f(x) = 3x^3 + 2x^2 - 4x - 7
3 2