Answers
The limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) is DNE
To take the limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6), we proceed as follows
Since we have the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) and we want to take the limit, we proceed thus,.
First, we divide both the numerator and denominator by x⁴. So,
lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) = lim x → ∞(x⁴ - 9x² + x)/x⁴ ÷ (x³ - x + 6)/x⁴
= lim x → ∞(x⁴/x⁴ - 9x²/x⁴ + x/x⁴ ÷ (x³/x⁴ - x/x⁴ + 6/x⁴)
= lim x → ∞(1 - 9/x² + 1/x³ ÷ (1/x - 1/x³ + 6/x⁴)
Now, taking the limit as x tends to infinity, we have that
= lim x → ∞1 - lim x → ∞9/x² + lim x → ∞1/x³ ÷ lim x → ∞1/x - lim x → ∞1/x³ + lim x → ∞6/x⁴
= (0 - 9/∞² + 1/∞³)/(1/∞ - 1/∞³ + 6/∞⁴)
= (0 - 9/∞ + 1/∞)/(1/∞ - 1/∞ + 6/∞)
= (∞ - 0 + 0)/(0 - 0 + 0)
= (∞)/(0)
= DNE
Related Questions
what is the circumference of a circle p PB=29m
Answers
If the diameter of the circle is 29 m, then the circumference is 29 pi m.
If the radius is 29 m, then the circumf. is 2(29 m) pi, or 58 pi m.
Answer:
The circumference of the given circle = 182.12 meters
Step-by-step explanation:
The circle P is given to us in which length of PB = 29 meter
Now, Since P is the center of the circle so PB will be the radius of the circle
So, Radius of the circle = 29 meter
We need to find the circumference of this circle with radius 29 meter
So, Circumference of the circle = 2π × radius of the circle
⇒ Circumference of the circle = 2 × 3.14 × 29
= 182.12 meter
Hence, The circumference of the given circle = 182.12 meters
what values make the inequality x+6/6-x<0 true?
Answers
It's C if you're taking the test
How many 1/4 cup portions can be served from 12 quarts of potato salad?
Answers
what is the unit rate of 1/5 and 1/4
Answers
Generally, questions like this do include that info.
Example: What is the unit rate of (1/5) white per (1/4 yellow)?
To determine this, divide (1/5) white) by (1/4 yellow)
1 white
-----------
5
------------------ = 0.20/0.25 white per yellow, or 0.8 white per yellow.
1 yellow
-----------
4
2/3×5/12=reduce lowest form
Answers
10 over 3 * 12 (multiply 2 * 5 so it can be 10)
10/36 ( multiply 3 * 12 so it can be 36)
5/18 (now simplify it)
Answer: 5/18.
2•4=8
_ _
3•4=12
8/12•5/12=5/18
5/18 is your answer.
Hoped I helped!
A summer camp has divided its campers into 8 groups of 9 campers.How many campers are at the summer camp?
Answers
Fill in each blank with the correct word to complete the sentence. The rules of the order of operations tells you to multiply and divide in order from _________ to ______
Answers
The rules of the order of operations tells you to multiply and divide in order from left to right.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The order of operations can be remembered by the acronym PEMDAS, which stands for: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. There are no parentheses in this problem, so start with exponents. Then, multiply and divide from left to right.
Hence, the rules of the order of operations tells you to multiply and divide in order from left to right.
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Suppose the graph of a line has a negative slope and a positive y-intercept. Through which quadrants does the line pass?
Answers
Since it has a positive y-intercept, it must go up to the left of the y-axis.
That means it must be in quadrant 2. Then as it crosses the y-axis, it must go into quadrant 1. Given enough length, it will have to go into quadrant 4 also.
The answer is: Quadrants 1, 2, 4
PLEASE HELP!!!!! I DONT UNDERSTAND!!!! :(
A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
Answers
[tex]\bf \stackrel{\textit{in years}}{P=25,000(1.0095)^t}\qquad \qquad \qquad \stackrel{\textit{in days}}{P=25,000(1.0095)^{\frac{t}{365}}}[/tex]
Which is another way to check the sum of 104 + 34 + 228 + 877? A. 877 – 104 + 34 + 228 B. 34 – 104 + 228 + 877 C. 877 + 228 + 34 + 104 D. 877 – 228 – 34 – 104
Answers
by adding the numbers in a different order would be a way to check so the answer is:
C. 877 + 228 + 34 + 104
A web server hosting company advertises 99.999 percent guaranteed network uptime. (a) how many independent network servers would be needed if each has 98 percent reliability? (round your answer up to the nearest whole number.) network servers (b) how many independent network servers would be needed if each has 89 percent reliability? (round your answer up to the nearest whole number.) network servers
Answers
a. The 50 independent network servers would be needed if each has 98% reliability.
b. Approximately 9 independent network servers would be needed if each has 89% reliability.
To calculate the number of independent network servers needed for a given level of reliability, we can use the following formula:
[tex][ \text{Number of servers} = \frac{1}{1 - \text{Reliability}} ][/tex]
a) For servers with 98% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.98} = \frac{1}{0.02} = 50 ][/tex]
Therefore, 50 independent network servers would be needed if each has 98% reliability.
b) For servers with 89% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.89} = \frac{1}{0.11} \approx 9 ][/tex]
Therefore, approximately 9 independent network servers would be needed if each has 89% reliability.
Find the inverse of each of the given functions.
f(x) = 4x − 12
f−1(x) = _x + _
Answers
f(x) = 4x − 12
f−1(x) =1/4 x + 3
The inverse of the function f(x) = 4x - 12 is f^-1(x) = (x + 12)/4.
Explanation:To find the inverse of the function f(x) = 4x - 12, we need to switch the roles of x and y and solve for y.
Step 1: Replace f(x) with y: y = 4x - 12.
Step 2: Swap x and y: x = 4y - 12.
Step 3: Solve for y: x + 12 = 4y.
Step 4: Divide both sides by 4: (x + 12)/4 = y.
Therefore, the inverse function is f-1(x) = (x + 12)/4.
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what percentage is 699 of 4736
Answers
(699/4736)*100
I need to know the three points of inflection
Answers
--------------------------------
--------------------------------
Explanation:
The inflection point is one where the graph changes from concave up to concave down, or vice versa. When x = c, the graph goes from concave down to concave up. For x = d, we go the opposite way from concave up to concave down. The value x = e is similar to x = c.
If a = (8.4∠39°) and b = (5.2∠50.4°), find the product a·b and the quotient a/b
Answers
In the case of the quotient: Divide 8.4 by 5.2 and then subtract 39 from 50.4 (degrees).
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answers
Answer:
The required equation of line is y=-6x-57.
Step-by-step explanation:
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where m is slope of the line.
It is given that a line that passes through (–9, –3) and has a slope of –6.
Substitute m=-6, x₁=-9 and y₁=-3 in the above equation.
[tex]y-(-3)=-6(x-(-9))[/tex]
[tex]y+3=-6x-54[/tex]
Subtract 3 from both the sides.
[tex]y=-6x-54-3[/tex]
[tex]y=-6x-57[/tex]
Therefore the required equation of line is y=-6x-57.
Answer:
D).y+3=-6(x+9)
Step-by-step explanation:
took it on edge
If I spoke with 800 customers in 40 hours how many customers did I speak to every 30 minutes
Answers
Answer:
10 customers were spoken to in every 30 minutes
Step-by-step explanation:
First, we convert 40 hours into minutes by multiplying it with 60 [as 1 hour = 60 minutes]
So, 40 hours = 40*60 minutes
= 2400 minutes
In 2400 minutes, number of customers served = 800
In 1 minute, number of customers served = [tex]\frac{800}{2400}[/tex]
In 30 minutes, number of customers served = [tex]\frac{800}{2400}*30[/tex]
= [tex]\frac{800}{2400} * \frac{30}{1}[/tex]
= [tex]\frac{800*30}{2400*1}[/tex]
= [tex]\frac{24000}{2400}[/tex]
= 10
So,
10 customers were spoken to in every 30 minutes
Final answer:
You spoke with 10 customers every 30 minutes.
Explanation:
To find out how many customers you spoke to every 30 minutes, we can set up a proportion. We know that you spoke with 800 customers in 40 hours, which is equivalent to 2400 minutes. So, the proportion is:
800 customers / 2400 minutes = x customers / 30 minutes
Now, we can cross-multiply and solve for x:
800 * 30 = 2400 * x
x = 800 * 30 / 2400
x = 10
Therefore, you spoke with 10 customers every 30 minutes.
Which expression represents the distance between 4.7 and −11.2 on the number line? Drag and drop the correct expression into the box.
Answers
Answer:
15.9Step-by-step explanation:
[tex]\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9[/tex]
The distance between 4.7 and -11.2 on the number line is 15.9.
Explanation:The distance between two points on a number line can be found by taking the positive difference between their coordinates. In this case, the distance between 4.7 and -11.2 is found by subtracting the smaller number from the larger number and taking the absolute value.
Distance = |-11.2 - 4.7| = |-15.9| = 15.9
Therefore, the correct expression is Distance = 15.9.
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What is the probability of rolling a sum of 8 on a standard pair of six-sided dice? express your answer as a fraction or a decimal number rounded to three decimal places, if necessary?
Answers
2+6
3+5
4+4
5+3
and 6+2.
Note: the order does matter, because you roll two die. This means the first die has a number and the second die also has a number. 2 on 1st dice and 6 on 2nd dice would be a different combination than 2 on 2nd dice and 6 on 1st dice.
Now we calculate the probability of getting a number 2 through 6 on the first dice: which is 5/6.
Then calculate the probability of getting a number that pairs up with the first number to make 8: *Note: once you get a number 2 through 6, there is only one other number that you can roll to make 8. This means the probability of getting a match would be 1/6 on the 2nd dice.
Finally, multiply the two fractions we got earlier: 5/6 x 1/6 = 5/36
Your probability would be 5/36 in fraction form, 13.89% in percent form, or 0.139 in decimal form rounded 3 places.
Hope this helps, and May the Force Be With You!
-Jabba the Hut
The probability of rolling a sum of 8 on a pair of standard six-sided dice is 5 out of 36, or 0.139 rounded to three decimal places.
Explanation:The subject of your question is
probability
, a topic in Mathematics. To solve this, we want to know the total number of outcomes when two dice are rolled; which is 6*6 = 36. Then we determine how many of these outcomes result in a sum of 8. Upon careful examination, we find that there are 5 (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the
probability of rolling a sum of 8
on a standard pair of six-sided dice is 5 out of 36, which can be expressed as
5/36 or 0.139
rounded to three decimal places.
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Lane's arm span is 61 inches. If his height is 1⁄4 foot longer than his arm span, how tall is he?
Answers
1 foot = 12 inches
1/4 foot = 12/4 = 3 inches
61 +3 = 64 inches tall ( 5 ft 4 inches)
The graph below represents the price of sending video messages using the services of a phone company. What is the constant of proportionality?
Answers
In the question given above, the constant of proportionality is 24. To determine the constant of proportionality, look at the graph and take note of each price and the number of video it can send.
From the graph, it can be seen that, 48 cents will send 2 video messages, 96 cents will send 4 messages, 144 cents will send 6 messages and 192 cents will send 8 messages.
48/2 = 24
96/4 = 24
144/6 = 24
192/8 = 24.
What is the value of x in the solution to the following system of equations?
x − 2y = 2
3x + y = 6
Answers
x - 2y = 2 (1)
3x + y = 6 (2)
From (1), obtain
x = 2y + 2 (3)
Substitute (3) into (2).
3(2y + 2) + y = 6
6y + 6 + y = 6
7y = 0
y = 0
From (3), obtain
x = 2*0 + 2 = 2
Answer: (2, 0) or x=2, y=0
To find the value of x in a system of equations, you can use the substitution or elimination method. In this case, x = 2 is the solution.
To find the value of x in the system of equations x − 2y = 2 and 3x + y = 6, we can use the method of substitution or elimination.
Substitution method:
From the second equation, y = 6 - 3x.Substitute y = 6 - 3x into the first equation: x - 2(6 - 3x) = 2.Solve for x: x - 12 + 6x = 2, 7x = 14, x = 2.Therefore, the value of x in the solution to the system of equations is x = 2.
the poster you are giving your friend is in a cardboard tube with a 2 in diameter and 26 in length. will a rectangular piece of wrapping paper that is 8 in by 28in completely cover the tube
Answers
The value of the 8 in 8.4 is 100 times greater than the 8 in?
Answers
Final answer:
The 8 in the number 8.4 has a value that is 100 times greater than the 8 in the number 0.084. The first 8 represents 8 ones, while the second represents 8 hundredths.
Explanation:
The value of the 8 in 8.4 is 100 times greater than the 8 in 0.084. To understand why, let's remember that each position in a decimal number has a place value that is 10 times less than the place value to its left. For instance, in the number 8.4, the 8 is in the ones place, meaning its value is 8 ones or '8'. However, in the number 0.084, the 8 is in the hundredths place, so its value is 8 hundredths or '0.08'.
Therefore, when comparing the two eights, we see that:
The 8 in 8.4 equals 8 ones (8 × 1 = 8).
The 8 in 0.084 equals 8 hundredths (8 × 0.01 = 0.08).
To find a number whose 8 is worth 100 times less than the 8 in 8.4, we need the 8 to be two places to the right of the decimal point, which is the hundredths place. The number 0.084 satisfies this because 8 ones (the value of the 8 in 8.4) are 100 times greater than 8 hundredths (the value of the 8 in 0.084).
Which expression is equivalent to 6 – (–8)?
–6 + 8
–6 + –8
6 + –8
6 + 8
Answers
Answer:
A
Step-by-step explanation:
Assign point_dist with the distance between point (x1, y1) and point (x2, y2). the calculation is: distance = squarerootof( (x2 - x1)2 + (y2 - y1)2 ). sample output for the given program:
Answers
The program is an illustration of functions
Functions are collections of defined program statements, that are executed when evoked
The program in Python, where comments are used to explain each line is as follows:
#This imports the math module
import math
#This defines the function
def calculateDistance(x1,y1,x2,y2):
#This calculates the distance between the points
dist = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
#This returns the calculated distance
return dist distance
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Solve for n: a= p(1+nr)
Answers
- _ + _
r pr
A submarine hovers at 240 meters below sea level.if it descends 160 meters and then ascends 390 meters,what is the new position
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Expanded form 13,936
Answers
13000 + 900 + 30 + 6 = 13936
10,000+3,000+900+30+6= 13,936
And the words is thirteen thousand nine hundred and thirty-six
It will help you:)
12<3b or 2b+14<4 please help
Answers
12/3 < b
b > 4
For 2b + 14 < 4 lets solve it:
2b < 4 - 14
2b < -10
b < -10/2
b < -5