To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we must show how the function grows in comparison to x^3 asymptotically.
To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we need to show two things:
1. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex]
For a function to be [tex]\omega(x^3)[/tex], it needs to grow faster than [tex]x^3[/tex] asymptotically. This requires that the ratio of the function to [tex]x^3[/tex] tends towards infinity as x approaches infinity.
Consider:
[tex]\lim_{x \to \infty}[\frac{f(x)}{x^3} ] = \lim_{x \to \infty}[ \frac{x^3-1000x^2+x-1}{x^3} ][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
Since the limit does not tend to infinity but instead tends to 1, f(x) is not ω(x^3). We made a mistake in our earlier assumption; let's correct this in the next point.
2. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]o(x^3)[/tex]
To show that f(x) is [tex]o(x^3)[/tex], the ratio of f(x) to [tex]x^3[/tex] should tend to zero as x tends to infinity.
Consider:
[tex]\lim_{x \to \infty} [\frac{f(x)}{x^3}] = \lim_{x \to \infty}[\frac{x^3-1000x^2+x-1}{x^3}][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
This indicates that the limit tends to 1 and not 0, hence f(x) is not [tex]o(x^3)[/tex] either. We can see in both cases that the limits did not meet the required criteria for [tex]\omega(x^3)[/tex] or [tex]o(x^3)[/tex], implying a misunderstanding in the problem setup.
Which expression represents the distance between −14.6 and −5.2 on the number line?
Answer:
9.4
Step-by-step explanation:
We are given that two integers -14.6 and -5.2
We have to find distance between -14.6 and -5.2.
Difference between =-5.2-(14.6)
Difference=-5.2+14.6=9.4
Distance is the absolute value of 9.4
Therefore,
[tex]\mid 9.4\mid =9.4[/tex]
Distance between -14.6 and -5.2 is 9.4
Joy organized a wedding.
Guests had to choose their meal from beef, chicken or vegetarian.
1/3 of the guests chose beef
5/12 of the guests chose chicken
23 of the guests chose vegetarian
How many guests were at the wedding?
one integer is 30 more than another integer if the difference between the larger and twice the smaller is 8 find the integers
The sum of two numbers is 43 . The smaller number is 19 less than the larger number. What are the numbers?
By setting up a system of equations, we find that the larger and smaller numbers in question are 31 and 12, respectively. We solve for the larger number first and then use it to find the smaller number.
Explanation:To solve this problem, we can use variables to represent the two unknown numbers. Let's call the larger number x and the smaller number y. We have two pieces of information that can be turned into mathematical equations:
Now we can substitute the second equation into the first one to solve for x:
x + (x - 19) = 43
Simplifying the equation, we get:
2x - 19 = 43
Adding 19 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we have the value of x, we can find y:
y = 31 - 19
This gives us:
y = 12
Therefore, the larger number is 31 and the smaller number is 12.
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f + g)(x).
A. 3x2 + 8
B. 3x2 – 6
C. x2 – 6
D. x2 + 8
Which of the binomials below is a factor of this trinomial? x^2-7x-44
Answer:
C. (x -11)
Step-by-step explanation:
The given trinomial is [tex]x^2 - 7x - 44[/tex]
Let's factor it. To find factor, we need to find the factors of -44 such that when you add them, we have to get -7
-44 = -11*4
- 7 = -11 + 4
so the correct factors are -11 and 4
Now we can write the middle term - 7x = -11x + 4x
[tex]x^2 - 7x - 44 = x^2 - 11x + 4x - 44[/tex]
Now let's group the first two terms and second two terms and factor it.
= x(x - 11) + 4(x - 11)
Here (x-11) is common factor, so we can take outside and rewrite.
= (x - 11)(x + 4)
So the factors are (x - 11) and (x + 4)
Answer is C. (x -11)
What does X equal?
15= x/6 - 1
Find all the real cube roots of 1000/27
10/3
10/9
-10/9
-10/3
Answer:
10/3
Step-by-step explanation:
Simone is in a bike a thon for a fundraiser. she recives 15 dollars. for each mile she bikes if she wants to raise 510 dollars how many miles does she need to bring ke
5 (9/12 - 1/4) + 0.5
what is 4.333333333 as a fraction.
I need this answer right now!!
All but two of the here amid’s built by the ancient Egyptians have faces inclined at 52° angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 m. How tall was the pyramid, assuming it’s faces were inclined at 52°? Round your answer to the nearest meter.
A) 25m
B) 32m
C)52m
D) 105m
How can i use decimal models to add decimals?
Joe tapped his maple tree to get syrup. The tree filled 3/4 of a cup in 1/2 hour.At what rate does syrup flow from the tree?
The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data mentioned in the question,
The amount of syrup obtained from the tree = 3/4 cup
The time is taken to fill 3/4 cup = 1/2 hour
Then, the rate of flow of syrup will be,
(3/4) ÷ (1/2)
3/4 × 2/1
= 6/4 = 3/2
It can also be written in mixed fraction form,
= 1 1/2
To know more about arithmetic operations:
https://brainly.com/question/25277954
#SPJ2
convert 220 from degrees to radians
The conversion of the given degrees 220° is equal to 11π/9 radians approximately.
To convert degrees to radians, use the following formula:
radians = degrees × (π / 180)
Let's apply this formula to convert 220 degrees to radians:
radians = 220 × (π / 180)
radians = 220π / 180
Now, to simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 20:
radians = (220/20)π / (180/20)
radians = 11π / 9
Therefore, 220 degrees is equal to approximately 11π/9 radians.
learn more about degrees here
brainly.com/question/29117074
#SPJ6
When solving for a system of equations, if you get an answer of 6=0, what does this solution mean regarding the solution to the system ?
Naomi has 50 red beads and white beads. The number of red beads is 1 more than 6 times the number of white beads. How many red beads does Noami have?
To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How many quarts of lemonade did you make?
To make lemonade, using one gallon of water, four quarts of lemon juice, and 32 ounces of honey, you would make 34 quarts of lemonade.
Explanation:First, notice that gallons are larger than quarts. You are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 4 quarts in a gallon, so your conversion factor is 4. Now, multiply. Take the given number of gallons and multiply by 4.
8(1/2) x 4 = (17/2) x (4/1) = 68/2 = 34
The answer is 8(1/2) gallons - 34 quarts.
Price Tax Rate Tax
$199 5%
$4,750 6%
$99.50 4.7%
$19.88 6.9%
$8.95 7.2%
$14.27 6.8%
$544.38 4.2%
$7.49 8.1%
$28.56 7.5%
$14.98 4.9%
199 *0.05 = 9.95
4750 * 0.06 = 285
99.50 * 0.047 = 4.68
19.88 * 0.069 = 1.37
8.95 * 0.072 = 0.64
14.27 * 0.068 = 0.97
544.38 * 0.042 = 22.86
7.49 * 0.081 = 0.61
28.56 * 0.075 = 2.14
14.98 * 0.049 = 0.73
What would you do isolate the variable in the equation below,using only one step?
X-3=7
Select the correct answer below.
A.add 7 to both sides
B. Subtract 3 from both sides of the equation
C.add 3 to the left, 7 to the right.
D.add 3 to both sides
You measure the width of a doorway and find that it is 0.93 m wide. Find the greatest possible error of your measurement
Answer:
0.5 m
Step-by-step explanation:
The greatest possible error is 1/2 of the unit you are measuring in.
We are measuring in meters; this means the greatest possible error is 0.5 m.
Answer:
The right answer is 0.005m
Step-by-step explanation:
The greatest possible error in a measurement is the half of the measuring unit, it is one hald of the precision unit.
To solve it first you should recognize the measurement unit, in this case meters.
Then, because it is 0.93, you should notice that the last decimal occupies the place of the hundredth, so the GPE might be: 0.01/2 equal to 0.005, your answer.
What is difference between 164 and 220
The difference between 164 and 220 is 56.
The difference between 164 and 220 is 56. In mathematical terms, you calculate the difference by subtracting the smaller number from the larger one:
220 - 164 = 56.
Cookies are sold singly or in packages of 10
or 30
.
With this packaging, how many ways can you buy 60
cookies?
heather has 500 dollars in her savings account she withdraws 20 dollars per week for gas write an eqaution heather can use to see how many week it will take her to have a balance of 220 dollars
We draw a random sample of size 36 from a population with the standard deviation 3.5. if the sample mean is 27, what is a 95% confidence interval for the population mean?
The only way to sober up after drinking is
The body metabolizes and eliminates alcohol at a fixed rate, which can only be sped up with time. Hydrating and eating food may make you feel better, but they do not speed up the process of becoming sober.
Explanation:The only way to sober up after drinking is to allow time for your body to metabolize and eliminate the alcohol. No amount of coffee, water, or food can speed up this process. The liver processes alcohol at a fixed rate, and it takes about one hour to metabolize one standard drink. Other factors such as sex, weight, and age can affect this rate, but ultimately, getting sober just takes time. While waiting to sober up, hydrating and eating food can make you feel better, but doesn't actually speed up the sobriety process.
Learn more about Sobering Uphttps://brainly.com/question/1204181
#SPJ6
if 152 divided by x equals 36 what would x be?
What is the value of 2 in 0.812
The place of the digit 2 in the decimal number will be hundredths place.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The decimal number is given below.
⇒ 0.812
The place after the decimal starts from the tenths, hundredths, thousandths, and so on.
The place of the digit 2 in the decimal number will be hundredths place.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ3
a spool of ribbon has 18 feet on it. pieces measuring of 8 inches will be cut from the spool of ribbon. how many 8 inch segments will be cut from the spool of ribbon
show work
By dividing the total length by the length of the pieces, we conclude that we can make 2 of these pieces.
How many 8 inch segments will be cut?To get this, we need to divide the total length by the length of the desired pieces, and then round to the next (lowest) whole number.
Then we get:
N = 18ft/8ft = 2.25
Rounding to the next whole number we get 2, so we conclude that with 18t of ribbon we can make 2 pieces of 8ft each.
If you want to learn more about divisions.
https://brainly.com/question/1622425
#SPJ2
how do you read this number. 7,654,321?