Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems. If the sequence diverges, enter DIV as your answer. cn=ln(4n−7/6n+4)
lim n→[infinity]cn=
Answers
The limit of the sequence cn that diverges by using the appropriate Limit Laws or theorems is ln(2/3).
What is limit?A limit is a fundamental concept in calculus that describes the behavior of a function as its input values approach a certain value, often infinity or negative infinity.
More specifically, the limit of a function f(x) as x approaches a number is the value that f(x) gets arbitrarily close to as x gets arbitrarily close to a. We denote the limit of f(x) as x approaches a by the notation:
\(\lim_{x \to \ a} f(x)\)
To determine the limit of the sequence c_n = ln((4n-7)/(6n+4)) as n approaches infinity, we can use algebraic manipulation and the properties of limits as follows:
\(cn = ln((4n-7)/(6n+4))\\= ln(4n/6n × (1-7/(4n))/(1+4/(6n)))\\= ln(2/3 × (1-7/(4n))/(1+2/(3n)))\\= ln(2/3) + ln((1-7/(4n))/(1+2/(3n)))\)
As n approaches infinity, the fraction (1-7/(4n))/(1+2/(3n)) approaches 1 since the denominator becomes much larger than the numerator. Therefore, we have:
\(\lim_{n \to \infty} (1-7/(4n))/(1+2(3n)) = 1\)
By the continuity of the natural logarithm function, we can then take the limit inside the logarithm and obtain:
\(\lim_{n \to \infty} cn = ln(2/3) + ln(1) = ln(2/3)\)
Therefore, the limit of the sequence cn is ln(2/3).
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Related Questions
what is p to the power of 2
Answers
Answer:
It really depends if there is more work with this, but of it is just p to the power of two. it would be p².
A circle has radius 6 units. for each arc length, find the area of a sector of this circle which defines that arc length.
1. 4π units
2. 5π units
3. 10 units
4. l units
Answers
Lucas wants to have at least $4,000 in his account. He has $2,500 to deposit into an account that earns simple interest at a rate of 6%. What is the fewest number of years it will take Lucas to reach his goal?
Answers
Answer:
6.25 years
Step-by-step explanation:
Simple interest = principal x time x interest rate
simple interest = $4,000 - $2,500 = $1,500
1500 = $4,000 x 0.06 x n
1500 = 240n
divide both sides by 240
n = 6.25 years
elements of {1,2,3,4,6,12} and {4,6,8,10}
Answers
Step-by-step explanation:
A ={1,2,3,4,6,12}
B={4,6,8,10
\(A \cup B=\){1,2,3,4,6,8,10,12}
use what you know about prisms to describe a pentagonal prism. include information about faces, edges, and vertices in your description.
Answers
The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.
A pentagonal prism is a prism with five rectangular sides and two top and bottom pentagonal bases. With 7 faces, 10 vertices, and 15 edges, it is a particular form of heptahedron. A pentagonal prism can have five sides due to its pentagonal bases. The pentagonal prism is also called Five-sided polygon prism in other name.
The pentagonal prism is a prism with five rectangular sides and two pentagonal base
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Answer:
The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.
Step-by-step explanation:
hope this helped!
There is 1 black ball and 2 white balls in the urn. We draw a ball, check its color and put it back in the urn. If the ball is white, we add another 1 black ball to the urn and if it is black we add 1 white ball. We draw a ball from the urn again, check its color and put it back into the urn. If the ball is black we add 2 black balls to the urn, and if it is white, 1 white ball. In the third round, we draw a single ball from the urn.
• What is the probability of drawing a white ball in the third round?
• What is the probability that the ball drawn in the first round was white if the ball drawn in the third round was white?
Answers
The probability of drawing a white ball in the third round is 7/12 or approximately 0.583.
Let's examine the possible scenarios for the color of the ball drawn in each round. In the first round, there are two possibilities: drawing a black ball (B) or drawing a white ball (W). If we draw a black ball in the first round, we add 1 white ball to the urn. If we draw a white ball, we add 1 black ball. So after the first round, the urn contains 2 black balls and 3 white balls. In the second round, there are now 5 balls in the urn: 2 black and 3 white. If we draw a black ball in the second round, we add 2 black balls to the urn. If we draw a white ball, we add 1 white ball. So after the second round, the urn contains 4 black balls and 4 white balls.
Now, in the third round, there are 8 balls in the urn: 4 black and 4 white. The probability of drawing a white ball is the number of favorable outcomes (white balls) divided by the total number of possible outcomes (total balls in the urn). Therefore, the probability of drawing a white ball in the third round is 4/8, which simplifies to 1/2 or 0.5.
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(Anyone?) it’s easy just do it pls
Answers
Answer:
if it's easy why dont you do it,that picture dont even take good
Which statements describe the solutions to ? Check all that apply. There are no true solutions to the radical equation. X = 2 is an extraneous solution. X = 3 is a true solution. There is only 1 true solution to the equation. The zeros of 0 = x2 – 5x 6 are possible solutions to the radical equation.
Answers
You can square both the sides and then use the formula for finding the roots of the obtained quadratic equation to find the solution needed.
The statements describing the solutions to the given equations are
Option C: x = 3 is a true solution.Option E: The zeroes(also called solutions) of \(x^2 - 5x + 6 = 0\) are possible solutions to the radical equation.How to find the solutions to a quadratic equation?Let the quadratic equation be \(ax^2 + bx + c = 0\)
Then the solution to this quadratic equation is given as
\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
What are extraneous solutions?Those values of the variables who come out behaving like solutions but when tested, doesn't get proved as solutions to the given equation are called extraneous solutions.
Using that above conclusion to find the solutions to the given equationSolutions to an equation means those values of the unknown for which the equation is true.
The given equation is
\(\sqrt{x-2} -4 = x - 6\)
Converting that equation to quadratic form, we get
\(\sqrt{x-2} -4 = x - 6\\\\\sqrt{x-2} = x - 2\\\)
From the obtained equation, we can see that x-2 is such a number whose square root is it itself. It is true for 2 numbers only.
First 1, and second 0.
Putting these values, we get
\(x-2 = 1\\x = 2+1 = 3\\\\x-2 = 0\\x = 2\)
Thus, there are two solutions to the given equation. They are x = 2, and x = 3
Testing both the solutions by putting them in the given equation.
Case 1: x = 2
\(\sqrt{x-2} -4 = x - 6\\\sqrt{2-2} - 4 = 2 - 6\\0-4 = -4\\-4 = -4\)
This is correct equality, thus, x = 2 is a correct solution.
Case 2: x = 3
\(\sqrt{x-2} -4 = x - 6\\\\\sqrt{3-2} - 4 = 3 - 6\\1 - 4 = -3\\-3 = -3\)
This is correct equality, thus, x = 3 is a correct solution.
The zeroes(also called solutions) of \(x^2 - 5x + 6 = 0\) is found as:
\(x^2 - 5x + 6 = 0\\x^2 - 3x - 2x +6 = 0\\(x-2)(x-3) = 0\\x = 2, x = 3\)
Thus, the The zeroes(also called solutions) of \(x^2 - 5x + 6 = 0\) are possible solutions to the radical equation given.
Thus,
Option C: x = 3 is a true solution.Option E: The zeroes(also called solutions) of \(x^2 - 5x + 6 = 0\) are possible solutions to the radical equation.Learn more about extraneous solutions here:
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Answer:
C and E are the correct answers.
Step-by-step explanation:
It's correct on Edgen. (2022)
. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answers
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
Condense to a single logarithm with a leading coefficient of
1.
ln(3) + ln(x) + ln(y)
Answers
The condensed form of the given logarithmic expression ln(3) + ln(x) + ln(y) is: ln(3*x*y)
To condense the given logarithmic expression to a single logarithm with a leading coefficient of 1, we can use the product property of logarithms.
The product property states that the sum of two logarithms with the same base is equivalent to the logarithm of the product of the two numbers.
Using this property, we can combine the three logarithmic terms in the given expression: ln(3) + ln(x) + ln(y) = ln(3*x*y)
Therefore, the condensed form of the given logarithmic expression is:
ln(3*x*y). This is a single logarithm with a leading coefficient of 1, as required.
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A rectangle has one side of 6 cm. How fast is the area of the rectangle changing at the instant when the other side is 13 cm and increasing at 3 cm per minute
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The area of the rectangle is changing at a rate of 18 cm²/min at the instant when the other side is 13 cm and increasing at 3 cm per minute.
To solve this problem, we need to use the formula for the area of a rectangle, which is A = lw, where l is the length and w is the width.
We know that one side of the rectangle is 6 cm, so we can call that the width (w). The other side is increasing at a rate of 3 cm per minute, so we can call that the length (l) and represent it as l(t) = 13 + 3t, where t is the time in minutes.
To find how fast the area (A) of the rectangle is changing, we need to take the derivative of the area formula with respect to time:
dA/dt = d/dt (lw)
dA/dt = w dl/dt + l dw/dt
Now we just need to plug in the values we know:
w = 6 cm
l = 13 + 3t cm
dw/dt = 0 (since the width is not changing)
dl/dt = 3 cm/min (since the length is increasing at a rate of 3 cm per minute)
dA/dt = 6(3) + (13 + 3t)(0)
dA/dt = 18 cm^2/min
So the area of the rectangle is increasing at a rate of 18 cm^2 per minute when the width is 6 cm and the length is increasing at a rate of 3 cm per minute to reach 13 cm.
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Convert 3.9m^2 into cm^2
I will leave good review!
Answers
Answer:
Step-by-step explanation:
To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.
So,
3.9 m² = 3.9 × (100 cm / 1 m)²
3.9 m² = 3.9 × 10,000 cm²
3.9 m² = 39,000 cm²
Therefore, 3.9 square meters is equal to 39,000 square centimeters.
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 7/10.
There are 42 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.
Answers
There is 60 total number of marbles in the bag for the probability of selecting a red marble is 7/10.
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
let the total possible outcome = x
probability of selecting a red marble = P(R) = 7/10
Given that there are 42 red marbles tgen:
42/x = 7/10
x = (42 × 10)/7 {cross multiplication}
x = 420/7
x = 60
Therefore, given the probability of selecting a red marble to be 7/10, the total number of marbles in the bag is derived to be 60
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what is the answer to the question 6*9+6+9?
Answers
Answer:
69
Step-by-step explanation:
6 × 9 + 6 + 9 = 69
Please give me Brainlest!
Answer:
69
Step-by-step explanation:
Original Equation:
6 · 9 + 6 + 9 = ?
Multiply 6 and 9
54
Plug this value back into the equation
54 + 6 + 9
Add 54 to 6
60
Plug this value back into the equation
60 + 9
69
Hope I helped :)
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TIME SERIES models attempt to predict the future by using historical data.
a. true b. false
Answers
The given statement is true because Time series models are statistical models that analyze and predict future values based on patterns and trends observed in historical data. Option A
The underlying assumption of time series analysis is that the future values of a variable can be predicted based on its past behavior. By examining the historical data, time series models identify patterns, trends, and seasonal variations that can help forecast future values.
There are various types of time series models, including autoregressive integrated moving average (ARIMA), exponential smoothing models, and seasonal decomposition of time series (STL). These models use different mathematical techniques to capture and analyze different aspects of the time series data.
The main goal of time series analysis is to make accurate predictions or forecasts of future values. By leveraging the patterns and trends observed in the historical data, these models provide insights into potential future outcomes.
Time series models are widely used in fields such as economics, finance, meteorology, stock market analysis, and demand forecasting, among others.
Option A
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a line with the a slope of -1 passes through the point 0, -3 what is its equation in slope intercept form
Answers
Answer:
y = -x -3
Step-by-step explanation:
Slope intercept form is in the form y= mx+b where m is the slope and b is the y intercept
Plug in the values from the problem
I REALLY NEED HELP PLEASE (exponents)
Answers
Answer:
A. or B. im pretty sure a tho try it
Step-by-step explanation:
5e = e + 10 Please help with this
Answers
Five e minus one e equal to ten
Four e equal to ten
e equal to ten over four
e equal to 2.5
stephan drove to his aunt's house at 60mph. he made the reutrn trip, over the same roadway, at 40mph. what was stephen's
Answers
Stephen's average speed for the round trip was 48 mph.
To find Stephen's average speed, we can use the formula:
Average Speed = Total Distance / Total Time
Let's assume the distance from Stephen's house to his aunt's house is 'd' miles.
On the way to his aunt's house, Stephen traveled at a speed of 60 mph. So the time taken for this leg of the trip is given by:
Time = Distance / Speed = d / 60
On the return trip, Stephen traveled at a speed of 40 mph. So the time taken for this leg of the trip is:
Time = Distance / Speed = d / 40
The total time for the round trip is the sum of the times for the outward and return trips:
Total Time = d / 60 + d / 40
To find the average speed, we divide the total distance by the total time:
Average Speed = Total Distance / Total Time
The total distance for the round trip is 2d (since it's the same roadway for both trips).
Average Speed = 2d / (d / 60 + d / 40)
Simplifying this expression, we get:
Average Speed = 2d / ((3d + 2d) / 120) = 2d / (5d / 120) = 2d * 120 / 5d = 240 / 5 = 48 mph
Therefore, Stephen's average speed for the round trip was 48 mph.
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The length of a rectangle is 4 centimeters is longer than its width. What are the possible integral widths if the area of the rectangle is less than 437 square centimetres?
Answers
Answer: 23
Step-step by explanation:
w(w+4)=437
w^2+4w-437=0
(w+23)(w-19)=0
w=19,-23
w<19
l<23!!
The possible integral width of the rectangle is 23.
What is a rectangle?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Given that the length of a rectangle is 4 centimeters is longer than its width. The area of the rectangle is less than 437 square centimeters
The width of the rectangle will be calculated as below:-
w(w+4)=437
w²+4w-437=0
(w+23)(w-19)=0
w=19,-23
w <19
w < 23
Therefore, the possible integral width of the rectangle is 23.
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find the next numbers 5, 1, 7, 0, 9, -1, 11...
Answers
Answer:
7,13,6
Step-by-step explanation:
you must take the number minus 4 then add 6 minus 7 then add 9, minus 10 then add 12.
Suppose 35% of students in a class have blue eyes. Five blue-eyed students join the class. Now 48% of the students have blue eyes. How many students were originally in the class?
Answers
Answer:
x : 35
x +5 : 48
35x+175=48x
175= 48x-35x
13x=175
x=175/13
x=13 students
if f(x)=10(2) then which of the following represents the value of f (0)
Answers
Answer:
< x < 10
Step-by-step explanation:
that answer would be
A pentagon has angle measures of 105°, 101°, 112° and 113°. What must the fifth angle measure?
The fifth angle measures is what?
Answers
Answer:
109
Step-by-step explanation:
Pentagon can be represented with 3 triangles:
A+B+C+D+E=3×180
105+101+112+113+E=540 => E=109
The reciprocal of 1/4 as a fraction Please help fast
Answers
Answer:
4/1
Step-by-step explanation:
Hope this help :P
write five other iterated integrals that are equal to the given iterated integral. 0 < x< z, y < z < 1
Answers
The iterated integral can be expressed equivalently in five other ways, and those are:
1. ∫∫∫_R f(x,y,z) dz dy dx, where the region R is defined as 0 < x < z, y < z < 1.
2. ∫∫∫_R f(x,y,z) dz dx dy, where the region R is defined as 0 < x < z, y < z < 1.
3. ∫∫∫_R f(x,y,z) dy dz dx, where the region R is defined as 0 < x < z, y < z < 1.
4. ∫∫∫_R f(x,y,z) dy dx dz, where the region R is defined as 0 < x < z, y < z < 1.
5. ∫∫∫_R f(x,y,z) dx dz dy, where the region R is defined as 0 < x < z, y < z < 1.
The iterated integral ∫∫∫_R f(x,y,z) dz dy dx represents a triple integral over the region R, where the bounds of integration are defined as 0 < x < z and y < z < 1.
To express the same integral in different forms, we can simply rearrange the order of integration. This rearrangement is permissible as long as the integral is evaluated over the same region R.
So, in the five other iterated integrals provided:
1. ∫∫∫_R f(x,y,z) dz dy dx: Here, we integrate first with respect to z, then y, and finally x. The bounds of integration are 0 < x < z, and y < z < 1.
2. ∫∫∫_R f(x,y,z) dz dx dy: In this case, we integrate first with respect to z, then x, and finally y. The bounds of integration remain the same as 0 < x < z, and y < z < 1.
3. ∫∫∫_R f(x,y,z) dy dz dx: Here, we integrate first with respect to y, then z, and finally x. The bounds of integration are y < z < 1, and 0 < x < z.
4. ∫∫∫_R f(x,y,z) dy dx dz: In this case, we integrate first with respect to y, then x, and finally z. The bounds of integration remain the same as y < z < 1, and 0 < x < z.
5. ∫∫∫_R f(x,y,z) dx dz dy: Here, we integrate first with respect to x, then z, and finally y. The bounds of integration are 0 < x < z, and y < z < 1.
These different orders of integration provide equivalent representations of the original iterated integral, allowing for flexibility in evaluating triple integrals over the specified region R.
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Find the slope of the line segment shown.
Answers
The slope is the "rise over run" between any two points on the line.
Count out how much "up or down" vs "left or right" to find the slope:
We go up 5 and right 5, giving us the fraction
\(\dfrac{up~ 5}{right~ 5}=\dfrac{5}{5}=1\)
When counting, up and right are counted as positive; left and down are counted as negative.
Why is the perimeter of the parallelogram?
Answers
Answer:
the perimeter is 32 squares
Step-by-step explanation:
if log75 = 0.83 then log57 =
Answers
The values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.
We can use the logarithm properties to find the value of log57 given that log75 is 0.83.
One of the logarithm properties states that:
log(a * b) = log(a) + log(b)
Using this property, we can express log57 in terms of log75:
log57 = log(5 * 3 * 19)
Now, we can use the fact that log75 is 0.83 to find log5, log3, and log19, and then add them together to get the value of log57:
log57 = log(5 * 3 * 19)
log57 = log5 + log3 + log19
However, since the values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.
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The equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.
To find log57 using the given information log75 = 0.83, we can use the change of base formula:
if log75 = 0.83, then log57 ≈ 0.827. To find log57 using the given information log75 = 0.83, we can use the change of base formula:log_b(a) = log_c(a) / log_c
Here, we want to find log57 (log_7(5)) using the given information log75 (log_5(7)).
We can rewrite the change of base formula as:log_7(5) = log_x(5) / log_x(7)We know that log_5(7) = 0.83,
so we can substitute this value into the equation:log_7(5) = log_x(5) / 0.83
Now we can use any common base, like base 10 or base e, to find the value of log_7(5). Let's use base 10:log_7(5) = log_10(5) / log_10(7)Now
we can calculate the values of log_10(5) and log_10(7) using a calculator:log_10(5) ≈ 0.69897log_10(7) ≈ 0.84510
Now substitute these values back into the equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.
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What are the 2 theoretical quantities of ANOVA?
Answers
The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.
2. Within-group variance:
1. Between-group variance.
This is the variance that can be attributed to differences between the group means.
It is calculated by comparing the mean of each group to the overall mean of all the data points.
The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:
This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.
It is calculated by comparing the individual data points in each group to their respective group mean.
The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.
If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.
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