Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate the limit. Finally, find the limit analytically and compare your results with the estimates. (Round your answers in the table to three decimal places.)
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we have the function
\(f(x)=\frac{x+1}{x\sqrt[]{x}}\)Complete the table
Substitute each value of x in the given function to obtain the value of f(x0
so
For x=10^0=1
\(f(x)=\frac{1+1}{1\sqrt[]{1}}=2\)For x=10^1=10
\(f(x)=\frac{10+1}{10\sqrt[]{10}}=0.348\)For x=10^2=100
\(f(x)=\frac{100+1}{100\sqrt[]{100}}=0.101\)For x=10^3=1,000
\(f(x)=\frac{1000+1}{1000\sqrt[]{1000}}=0.032\)For x=10^4=10,000
\(f(x)=\frac{10000+1}{10000\sqrt[]{10000}}=0.010\)For x=10^5=100,000
\(f(x)=\frac{100000+1}{100000\sqrt[]{100000}}=0.003\)For x=10^6=1,000,000
\(f(x)=\frac{1000000+1}{1000000\sqrt[]{1000000}}=0.001\)therefore
\(\lim _{x\to\infty}f(x)=0\)see the attached figure below
as the value of x increases -----> the value of f(x) decreases
as x ----> ∞ f(x) ---> 0
Related Questions
please answer need help
Answers
Which table represents a linear function?
Answers
Answer:
First table from left.
Step-by-step explanation:
Equal step of a half.
1,7
2,9
3,13
4,21
Step-by-step explanation:This is the linear function graph i plotted the points
Identify if the line has a positive or negative slope. Calculate the slope of the line 2y = x - 8
Answers
Answer: m = 1/2
Step-by-step explanation: To find the slope of the line, we would first put the equation in y = mx + b form to get y by itself on the left side.
So divide both sides by 2 to get y = 1/2x - 4.
Now the slope is the coefficient of the x term which is 1/2.
This is a positive slope.
If g(x)=4x^2-16 were shifted 5 units to the right and 2 down hat would the new equation be
Answers
Answer:
This is the answer
Step-by-step explanation:
This is the solution, hope it helps
4 Amanda and Blake played a board game. In the game, Amanda had
$2,740 in play money and Blake had $3,560. Amanda had to give some
money Amanda had. How much play money did Blake have in the end?
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The amount of money Blake have in the end is 3560 + (2740 - x)
In the game Amanda had $2740 in play money and Blake had $3560 in play money.
Amanda had to give some money she possessed.
Let
what remains after Amanda gave the money = x
Therefore, Blake will have the following money at the end .
The amount she gave to Blake = (2740 - x)
Blake money = 3560 + (2740 - x)
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Solve each equation by completing the square.
d² - 24d + c
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Answer:
d² - 24d + c = (d - 12)² - 144 + c
solve the following two equation X+Y=5
X-2Y=2
Answers
Step-by-step explanation:
x=4 and y= 1 because of 4+1=5 and add 2y to both sides
x-2y+2y=2+ 2y
x=2y+2
4-2=2
\(\left \{ {{x+y=5} \atop {x-2y=2}} \right.\)
Here we have 2 equations in one system.
System of Equations/Simultaneous Equations are for finding the intercepts of both graphs.
We can solve these Simultaneous Equations in many ways. However, I'll be solving by substitution.
To solve by using substitution, we need to move either x or y to the another side. I'll move x term to another side for the first equation. (We'll substitute the first equation in the second.)
\(\left \{ {{y=-x+5} \atop {x-2y=2}} \right.\)
Now we substitute y = -x+5 in x-2y = 2
\(x-2(-x+5)=2\\\)
Then distribute -2 in (-x+5) | Note that multiplying the negative will get positive. |
\(x-2(-x+5)=2\\x+2x-10=2\\3x=2+10\\3x=12\)
We should get this. When we get this, we move 3 to divide 12 (Opposite when moving to another side so from plus to minus and from multiply to divide.)
\(x=4\)
But we are not done yet. We have to find the y-value. After all they are two variables equations.
If we want to find the y-value then we have to substitute x = 4 in any given equations. I'd suggest to substitute in the equation that doesn't have a coefficient with high value.
So I'll be substituting in x + y = 5 instead.
Substitute x = 4 in x + y = 5
\(4+y=5\\y=5-4\\y=1\)
Thus, we get both x and y value. Answer in either coordinate point or writing form.
Therefore, the answer is
x = 4 when y = 1 or (4,1)
Both works. Hope this helps.
4 7/9 x 3 3/4
Write answer as a fraction or as a whole or mixed number
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Answer:
Exact form: 215/12
decimal form: 17.916
mixed number: 17 11/12
Step-by-step explanation:
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $84.00
Markdown: 32%
The sale price is
Answers
Answer:
\(Sales\ Price = \$57.12\)
Step-by-step explanation:
Given
\(Price = \$84.00\)
\(Markdown = 32\%\)
Required
Determine the sales price
First, we calculate the markdown price.
This is calculated by multiplying the original price the markdown percentage
\(Markdown\ Price = \$84.00 * 32\%\)
Convert % to decimal
\(Markdown\ Price = \$84.00 * 0.32\)
\(Markdown Price = \$26.88\)
The sales price is then calculated as:
\(Sales\ Price = \$84.00 - \$26.88\)
\(Sales\ Price = \$57.12\)
Hence, the sales price after markdown is $57.12
For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml.
Required:
Give the margin of error and find a 95% confidence interval for the mean TRAP amount in young women represented by this sample.
Answers
Answer:
The margin of error is \(E = 6.9 \)
The 95% confidence interval is \( 26.5 < \mu < 40.3 \)
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The mean is \(\mu = 33.4 \ ng/ml\)
The standard deviation is \(\sigma = 19.6 \ ng/ml\)
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 1.96 * \frac{19.6 }{\sqrt{31 } }\)
=> \(E = 6.9 \)
Generally 95% confidence interval is mathematically represented as
\(\= x -E < \mu < \=x +E\)
=> \( 33.4 - 6.9 < \mu < 33.4 + 6.9 \)
=> \( 26.5 < \mu < 40.3 \)
Benson Automotive earned $69.46 interest on a $9,400 deposit in an account paying 4.5%. Find the number of days that the funds were on deposit. Round to the nearest whole dayLearning simple interest.
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The rate given is 4.5%, but it didn't say theperiod of the intereset. In this case, we normally implies that the interest is annual.
The equation for simple interest is as follows:
\(I=P\cdot r\cdot t\)Where P is the princiapal value, r is the rate and t is the time period in years, because the rate is annual.
We want to calculate t, so we can solve for it:
\(t=\frac{I}{P\cdot r}\)Ans we substitute the values:
\(t=\frac{69.46}{9400\cdot4.5\%}=\frac{69.46}{9400\cdot0.045}=0.164208\ldots\)That is, 0.164208... years.
In one normal year, we have 365 days, so the time in days is:
\(0.164208\ldots\cdot365=59.935\ldots\approx60\)So, the answer is 60 days.
The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by
(2x + 3)°. What is the value of x? What is the measure of each base angle?
x =
Each base angle measures
°.
Answers
Answer:
x=33 and angle=69
Step-by-step explanation:
just got it on a test
Measure of x = 69 degree.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that,
vertex angle = 42 degree
Angle of base angle = (2x + 3)°
Use the knowledge that the sum of the base angles in an isosceles triangle equals 180° minus the vertex angle to find the value of x.
Thus,
Vertex angle is,
(2x + 3)° + (2x + 3)° = 180° - 42°
Base angle + Base angle = 180° - 4x + 6 = 138
4x = 132 x = 33
We substitute x = 33 into (2x + 3)°
To determine the magnitude of each base angle:
Base angle equals (x + 3)°
Base angle = (2 x 33 plus 3).
Angle at base: 69° As a result, each base angle is 69°.
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28/a + 6 =
Plss I need help
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Answer:
\(\frac{28 + 6a}{a}\)
Step-by-step explanation:
Which table shows proportional relationship between x and y?
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Answer:
C
Step-by-step explanation:
For a relationship to be proportional, x/y needs to be the same for all rows.
5/8 is not 12/15
5/3 is not 15/11
3/8 is not 5/12.
The table C checks out with a ratio of 3:5
what is the average rate of change if this function interval x = -3 to x = 0
Answers
The average rate of change of the function, over the given interval is 2.
This question is incomplete, the complete question is:
What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.
What is the average rate of change over the interval?The average rate of change of f(x) over the interval [a,b] is expressed as;
\(\frac{f(b)-f(a)}{b-a}\)
Given that;
f(x) = 2x + 10Interval: [ -3, 0 ], a = -3 and b = 0We substitute our values into the expression above.
\(\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2\)
Therefore, the average rate of change of the function, over the given interval is 2.
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Which event is considered neither likely nor unlikely?
A, Rolling a number greater than 1 on a six-sided number cube.
B, Rolling a 1 on a six-sided number cube.
C, Getting heads when flipping a coin.
D, Choosing an X,Y, or Z from a bag containing all the letters of the alphabet.
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According to the information, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely.
Which event is considered neither likely nor unlikely?In probability, an event is considered likely if its probability is high, and it is considered unlikely if its probability is low. An event is considered neither likely nor unlikely if its probability is close to 0.5 or 50%. In this case we have to consider the probability of each option to establish a conclusion. Here is the analysis:
A, rolling a number greater than 1 on a six-sided number cube, has a probability of 5/6, which is greater than 0.5, so it is considered likely.B, rolling a 1 on a six-sided number cube, has a probability of 1/6, which is less than 0.5, so it is considered unlikely.C, getting heads when flipping a coin, has a probability of 1/2, which is equal to 0.5, so it is considered neither likely nor unlikely.D, choosing an X, Y, or Z from a bag containing all the letters of the alphabet, would depend on the specific contents of the bag. If the bag contains an equal number of each letter of the alphabet, the probability would be 3/26, which is less than 0.5, so it would be considered unlikely.According to the above, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely because its probability is exactly 0.5 or 50%.
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Find the volume of a sphere with a radius of 12.5cm. (Note: Take the value of π as 3.14.) Round your answer to the nearest thousandth, if necessary.
Answers
The volume of the sphere is approximately 8181.510 cm³.
The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.
It is a measure of the three-dimensional space that is contained within the sphere.
The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:
V = (4/3) × 3.14 × (12.5 cm)³
V ≈ 8181.51 cm³
The volume of the sphere is approximately 8181.510 cm³.
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Jo has a 10 GB monthly cell phone plan. Jo has used 8 GB in the first 10 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answers
Answer:
Step-by-step explanation:
1st 10 days - 8 GB
2nd 10 days - 8 GB
3rd 10 days - 8 GB
________________
30 days - 24 GB
EXPLORE ACTIVITY 2
TEKS 7.13.8
Analyzing a Family Budget
One way to present a budget is in a circle graph. You can see at a glance which
categories take the greatest part of the family's resources. You can also work
backward from a circle graph to figure out exactly how much money is in each
category.
Use the circle graph to complete
the table for the Baker family's
monthly budget. Their net
monthly income is $4,000.
STEP 1)
STEP 2
STEP 3
STEP 4
STEP 5
432 Unit 7
Enter the income in the table.
Enter the percent or amount of money for each
category from the circle graph in the table.
Calculate the amount of money or the percent
for each category in the table.
Determine which expenses are fixed and
which are variable. Place X's in the appropriate
columns.
Complete the Amount Available column.
Item
Net monthly income
means how much
income the family
has after taxes.
Net monthly
Income
Housing cost
Food
Savings
Entertainment
Clothing
Medical
Transportation
Emergency
fund
Amount
($)
Percent
(%)
Baker Family's Monthly Budget
Emergency fund
Transportation
(car expense,
bus passes)
$400
Medical
(insurance
and
additional
expenses)
$600
Clothing
8%
Entertainment
Savings
$320
Fixed
Variable
Amount
Expense Expense Available
($)
Housing
cost (house
payment and
Insurance!
$1,400
Food
15%
Answers
Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.
What happened during emergency repair of $305?4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.
5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.
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Full Question:
See attached image.
Reflect
4. Analyze Relationships One month, the family must make an
emergency car repair for $305. Are they able to pay for it out of the
fixed emergency fund for that month? If not, how can they afford it?
5. The family wants to make a trip to Houston to visit the NASA Space
Center. What are some ways they can save without using all of the
allotted $160 for entertainment
Which expression represents the total
surface area of the prism shown?
4(4) + 5(5)+7(7)
2(5-7)+2(4-7)+2(4.5)
4(5) + 4(7) + 5(7)
2(4 4) + 2(5.5) + 2(7.7)
5 cm
7 cm
4 cm
Answers
Determine the x intercepts of the piecewise function in the image that I sent.
Answers
To find the x intercept of the function, we would find g(x) = 0
To do this, we would set each expression in the piecewise function to zero and solve for x. We have
For
x/3 + 2 = 0
let us multiply both sides of the equation by 3. We have
x/3 * 3 + 2 * 3 = 0 * 3
x + 6 = 0
x = - 6
- 6 is less than - 1
- 6 < - 1
It satisfies the inequality. Thus, x = - 6 is in the domain
For
4x - 2 = 0
adding 2 to both sides of the equation, we have
4x - 2 + 2 = 0 + 2
4x = 2
Dividing both sides of the equation by 4, we have
4x/4 = 2/4
x = 1/2
x = 1/2 is less than 1. It is not in the domain of this equation. Thus, there is no x interscept at x = 1/2
Therefore, the x intercept of the piecewise function is (- 6, 0)
the bar graph below represents the number of each type of animal found in northern Pennsylvania forest by a researcher. If the researcher moved to a larger central Pennsylvania forest with about 1,000 total animals , how many beats should the researcher expect to see?
Answers
The number of bears that the researcher should be expected to see in the larger central Pennsylvania forest with about 1,000 total animals is given as follows:
95 bears.
How to obtain the number of bears?To obtain the number of bears in the larger forest, first we must obtain the proportion in the smaller forest.
The proportion is given by the number of bears divided by the total number of animals, both of these amounts given by the bar graph presented at the end of the answer.
The number of bears is given as follows:
20.
The total number of animals is given as follows:
20 + 70 + 30 + 90 = 210.
Meaning that the proportion of bears is of:
20/210.
Hence, out of 1000 animals, the expected number of bears is of>
20/210 x 1000 = 20000/210 = 95 bears.
Missing InformationThe bar graph is given by the image presented at the end of the answer.
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What is the order of magnitude for the following number 1.25 x 105 ?
A. 1.25
B. 10
C. 5
Answers
The order of the magnitude of the given number is a 5.
According to the statement
We have to find that the order of the magnitude.
So, For this purpose, we know that the
An order of magnitude is an exponential change of plus or minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation.
From the given information:
The number are 1.25 x 105
To find the order firstly solve it then
1.25 x 105
1.25 x 105 = 131.25
And in this according to the definition of the order of the magnitude:
The order is of the 5 numbers.
So, The order of the magnitude of the given number is a 5.
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Rolling a 6-sided die and counting the number of each outcome that occurs is a bionomial random variable. True or False? Which option gives the most accurate response?
Answers
Answer:
False.
Step-by-step explanation:
This is NOT an example of a binomial random variable, because a binomial random variable can only have TWO possible outcomes: success or failure. In the case of rolling a die, there are SIX possible outcomes: 1, 2, 3, 4, 5, or 6.
So, rolling a 6-sided die and counting the number of each outcome that occurs is NOT a binomial random variable.
Hope this helps!
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is not an example of the binomial random variable. This is because the binomial random variable can only have two possible outcomes, which is not true in the case of a die that had six faces and six outcomes for each through.
Although if the probability is needed to be calculated for the same digit occurring or not it can be calculated using the binomial random variable.
Hence, The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
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What is mJH
mJH = degrees
Answers
ytog8higfjfhlfiydd6ofudydyfof6f
tQuestion 9 Alex launched a ball into the air. The height of the ball can be represented by the equation
Answers
The height of the ball with respect to time is represented by the following equation
\(h(t)=-8t^2+40t+5\)Where h(t) is the height and t is the time in seconds.
Since it is a quadratic equation, let us compare it with the standard form of a quadratic equation.
\(f(x)=ax^2+bx+c\)Comparing the given equation with the standard form, the coefficients are
a = -8
b = 40
c = 5
Recall that the x-coordinate of the vertex is given by
\(\begin{gathered} -\frac{b}{2a} \\ -\frac{40}{2(-8)_{}} \\ \frac{40}{16_{}} \\ 2.5 \end{gathered}\)Recall that the y-coordinate of the vertex is given by
\(\begin{gathered} h(t)=-8t^2+40t+5 \\ h(2.5)=-8(2.5)^2+40(2.5)+5 \\ h(2.5)=-8(6.25)^{}+100+5 \\ h(2.5)=-50^{}+100+5 \\ h(2.5)=55 \end{gathered}\)So, the coordinates of the vertex are
\(vertex=(2.5,55)\)The coordinates of the vertex represent the highest point achieved by the ball.
The vertex tells us that the maximum height of the ball was 55 units and it occurred at 2.5 seconds.
This can be confirmed by looking at the graph of the given equation
As you can see from the above graph, the vertex is the maximum point of the graph that is (2.5, 55)
6. Find the areas of the rectangles with the following side lengths.
a. 5 in and 1/3 in
c. 5/2 in and 4/3 in
b. 5 in and 4/3 in
c. 2/5 in and 4/3 in
d. 7/6 in and 6/7 in
I need an explanation on how you got the answer
Answers
This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
Answers
Answer:
4.28%
Step-by-step explanation:
We Know
Last year you earned $72,400
This year you earned $75,500
What was the rate of change in your earnings since last year?
We Take
(75,500 ÷ 72,400) x 100 ≈ 104.28%
Then We Take
104.28 - 100 = 4.28%
So, the earning increased by about 4.28%.
A classroom floor has a perimeter of 132 feet. What is the perimeter in
yards?
Answers
Answer:
44 yards
Step-by-step explanation:
Formula :
divide the length value by 3
Write the equation of the line that passes
through the points (3, 1) and (-2, 6).
Answers
Answer:
x + y - 4 = 0
Hope this helps, if you need more of an explanation feel free to let me know!