Use the definition of Taylor series to find the Taylor series, centered at c, for the function.
f(x)=
1
x
, c=1
Answers
The Taylor series for f(x) = 1/x, centered at c=1, is:
1/(x-1) = Σ[n=0 to infinity] (-1)ⁿ * (x-1)ⁿ
The Taylor series for the function f(x) = 1/x centered at c = 1 using the definition of Taylor series. The Taylor series for a function f(x) is given by:
f(x) ≈ f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...
For f(x) = 1/x and c = 1, let's find the first few derivatives and their values at c = 1:
f(x) = 1/x
f'(x) = -1/x^2
f''(x) = 2/x^3
f'''(x) = -6/x^4
Now, evaluate them at c = 1:
f(1) = 1
f'(1) = -1
f''(1) = 2
f'''(1) = -6
Now we can plug these values into the Taylor series formula:
f(x) ≈ 1 - (x-1) + 2(x-1)^2/2! - 6(x-1)^3/3! + ...
Simplifying the expression, we get:
f(x) ≈ 1 - (x-1) + (x-1)^2 - (x-1)^3 + ...
This is the Taylor series for the function f(x) = 1/x centered at c = 1.
To learn more about derivative visit;
brainly.com/question/30365299
#SPJ11
Related Questions
Solve each equation using tables. Give each answer to at most two decimal places.
x²-7 x=11
Answers
The solution to the equation x² - 7x = 11 is approximately x = 8.0, rounded to two decimal places.
To solve the equation x² - 7x = 11 using a table, we can create a table with values of x and corresponding values of the expression x² - 7x. We will look for the x-value(s) that make the expression equal to 11.
Let's start by plugging in various values of x and calculating the corresponding values of x² - 7x:
| x | x² - 7x |
|-------|---------|
| -10.0 | 180.0 |
| -5.0 | 66.0 |
| 0.0 | -0.0 |
| 5.0 | -20.0 |
| 10.0 | -60.0 |
Based on the table, we can see that there is a change in sign from positive to negative, indicating that there is a solution between x = 5.0 and x = 10.0.
To find a more precise solution, we can use an incremental approach:
| x | x² - 7x |
|-------|---------|
| 6.0 | -6.0 |
| 6.5 | -10.25 |
| 7.0 | -15.0 |
| 7.5 | -20.75 |
| 8.0 | -28.0 |
Based on the more refined table, we can see that the expression x² - 7x becomes closer to 11 as x approaches 8.0. Therefore, the solution to the equation x² - 7x = 11 is approximately x = 8.0, rounded to two decimal places.
Visit here to learn more about decimal brainly.com/question/30958821
#SPJ11
HELP I NEED HELP ASAP
Answers
Answer:
b
Step-by-step explanation:
if two equations are the same at two different points, what can be said about the two equations?
Answers
Answer:
They are parallel
Step-by-step explanation:
They will have the same slope but never intersect
Which lists the ratios in order from greatest to least?
23:24, 11:12, 7:8
23:24, 7:8, 11:12
7:8, 23:24, 11:12
7:8, 11:12, 23:24
PLS HELP, ITS DUE VERY SOON
Answers
Answer:
A the first one
Step-by-step explanation:
hope this helps
A movie theatre marks up the price of popcorn 12 3/4 times the original cost. express 12 3/4 as a percent and decimal.
Answers
Answer:
Answer: F. 1,275% and 12.75.
Step-by-step explanation:
Ratios
Ratios are usually expressed as decimals, fractions, colon notation, and percentages.
For example, if the ratio of two quantities is 2, it can be expressed as:
2, 2/1, 2:1, 200%
To obtain the percentage expression, just multiply by 100%.
The price of the popcorn sold at a movie theatre was marked up as 12 3/4 times the original cost.
The mixed fraction can be converted to a decimal by just adding their parts as follows:
12 + 3/4 = 12.75
Now to express it as a percentage, multiply by 100%:
12.75 * 100% = 1,275%
Answer: F. 1,275% and 12.75.
according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
Answers
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
brainly.com/question/24138432
#SPJ4
find the euler equation that represents the relationship between current-period consumption and future-period consumption in the optimum.
Answers
The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.
In the context of consumption, the Euler equation can be expressed as:
u'(Ct) = β * u'(Ct+1)
where:
- u'(Ct) represents the marginal utility of consumption in the current period,
- Ct represents current-period consumption,
- β is the discount factor representing the individual's time preference,
- u'(Ct+1) represents the marginal utility of consumption in the future period.
This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.
Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.
To know more about marginal utility related question visit:
https://brainly.com/question/30841513
#SPJ11
Write three equivalent ratios for 12 to 18.
Answers
Answer:
2 to 3, 24 to 36, and 6 to 9
Step-by-step explanation:
First ratio:
We can find our first equivalent by finding the greatest common factor (GCF) of 12 and 18 and then by dividing both numbers by it. The GCF of 12 and 18 is 6. 12/6 = 2 and 18/6 = 3. Thus, one equivalent ratio is 2 to 3Second equivalent ratio:
We can also divide 12 and 18 by other shared factors, even though they're not the GCF. We know that 2 is a shared factor of both 12 and 18.12/2 = 6 while 18/2 = 9Thus, a second equivalent ratio is 6 to 9.Third equivalent ratio:
When we have a ratio, we're able to produce an equivalent by multiplying both numbers by the same number. We can try 2.12 * 2 = 24 and 18 * 2 = 36Thus, a third equivalent ratio is 24 to 36.PLEASE HELP, IVE BEEN STUCK ON THIS QUESTIon fOR 23 MINUTES , PLEASE INCLUD PART BIM GIVING ALL MY POINTS
Answers
Answer:
1:4 and 25%
Step-by-step explanation:
For every 4 items 1 medium sized item is bought. And that means that its 1/4 of all items bought, which can be converted to 25% medium items.
The circumference of a circle is 18.84 mi. What is the circle's diameter?
Answers
Answer:
I got 6 mi
hope I helped
Based on the passage, what is the best inference?
-John doesn’t want to see the show.
-John is happy about being given the ticket.
-John has trouble making decisions.
-John often makes decisions too quickly.
"I don't know what to do," John sighed and shrugged as he stared at the free ticket for tomorrow's show that he'd just been given. "I planned to go to the beach tomorrow."
Answers
Answer:
John has trouble making decisions.
Step-by-step explanation:
In the passage, it says the "I don't know what to do," John sighed and shrugged as he stared at the free ticket for tomorrow's show that he'd just been given. ,¨ indicates he´s having some trouble.
Answer:
John has trouble making decisions < 3
...................................................................................................................................
This is 100 % correct :'}
.................................................................................................................................
I know im late lol , but for the people who didnt know what the answer was this is the answer ! ;')
....................................................................................................................................
Have a nice day < 33 !
...................................................................................................................................
use Euler's method with a step size of 0.4 to approximate the solution of the differential equation y'=2xy; y(1)=2, at x=3
Answers
Answer:
Approximate solution is 541.
Step-by-step explanation:
y' = 2xy, Δx = 0.4.
Make a table:
x y y' y' Δx + y
1 2 4 4*0.4 + 2 = 3.6 <---this is the new y value.
1.4 3.6 10.08 7.632
1.8 7.632 27.48 18.624
2.2 18.624 81.95 51.70
2.6 51.70 268.85 159.24
3 159.24 955.44 541.4
I need help with this problem
Answers
Answer:
(3,4)
Step-by-step explanation:
Because that's where the two lines intersect.
Answer:
(3, 4)
Step-by-step explanation:
We have a graph with two intersecting lines.
When this question about the solution to the system comes up, to find the answer, you look at the point both lines are intersecting at.
Therefore, look at the graph.
The linear model P=3.75g+1.5 predicts the total cost, P, in dollars, to purchase g gallons of gas at a gas station. Based on the linear model, how much should it cost to purchase 12 gallons of gas?
Answers
Answer:
Answer is 46.50
Step-by-step explanation:
I look everywhere and said it was this hehe
If my phone bill is calculated using equation c= 50g +75 what is the value and interpretation of the slope of this equation? C= cost and g= gigabytes of data used each month
Answers
Answer:
The value of the slope in this equation is 50
The interpretation is that the rate of change in the cost of the phone bill per unit change in gigabytes of data used each month is 50
Step-by-step explanation:
To answer this question, we need to compare the given equation with the equation of a straight line graph.
The equation we have is;
c = 50g + 75
comparing this with the equation of a straight line, we have
y = mx + c
where m represents the slope and c is the y-intercept
So comparing both, the slope of the equation is 50.
The slope is always the co-efficient of the value on the x-axis
So what does this mean?
The slope also called the gradient represents the rate of change of the y-term divided by the rate of change of the x-term. In simpler terms, when we talk of the slope, we mean the rate of change of the y term per the unit change of the x-term.
So what we mean in this case is the rate of change in cost of the phone bill per unit change in gigabytes of data used each month is 50
Write an equation that would have the restriction x ≠ 4
Answers
The equation, more specifically the rational equation which will have the restriction x ≠ 4 as required in the task content is; y = (x + 2)/(x - 4).
Which equation is an example of one which will have a restriction of x ≠ 4 as required in the task content?It follows from the task content that the equation which will have the restriction x ≠ 4 is to be determined.
The equation in discuss can best be in the form of a rational equation.
Since rational equations are restricted on their domains by values of x which renders the denominator of the equation equal to zero as the equation is undefined at this point.
The equation should therefore have denominator of this sort; x - 4 such that; x = 4 renders the function undefined.
Ultimately, the equation that would have the restriction x ≠ 4 is;
y = (x + 2)/(x - 4)
Read more on domain of a rational equation;
https://brainly.com/question/26500180
#SPJ1
What do we do to both sides of this equation to solve?
5x=20
Question 3 options:
Add 5 to both sides
Subtract 5 from both sides
Multiply both sides by 5
Divide both sides by 5
Answers
Hello there! :)
Answer:
Divide both sides by 5
Step-by-step explanation:
we are given an equation 5x=20.
First, Add 20 to both sides
\(\boxed{x=\frac{20}{5} }\)
Then, Divide both sides by 5.
\(\boxed{x=4}\)
Divide 20 by 5 to get 4.
And there you go Our answer is Divide by sides by 5.
-Hope this helps
-Have an awesome weekend :)
\(-Yuri-\)
Which could be the resulting equation when elimination is used to solve the given system of equations?
5a+5b-25
(-5a+5b-35
O 10a = 60
O 10b = 60
0-10 a = 60
-10b = 60
Answers
Answer:
10b=60 is correct
Step-by-step explanation:
What are like terms examples?
Answers
Step-by-step explanation:
Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.
Your local radio station is having their yearly music player and concert ticket giveaway. For one minute, every 5^\text{th}5 th 5, start superscript, start text, t, h, end text, end superscript caller will win a music player and every 7^\text{th}7 th 7, start superscript, start text, t, h, end text, end superscript caller will win concert tickets.
Answers
Complete question :
Your local radio station is having their yearly music player and concert ticket giveaway. For one minute, every 5th
5, start superscript, start text, t, h, end text, end superscript caller will win a music player and every 7th
7, start superscript, start text, t, h, end text, end superscript caller will win concert tickets.
You were just the first caller to win both a music player and concert tickets!
What number caller were you?
Answer:
35th Caller
Step-by-step explanation:
Given that:
Every fifth caller wins a music player ;
Every 7th caller wins a concert ticket
The first caller to win both prizes will be ;
The caller whose number corresponds to the lowest common multiple value of 7 and 5
The lowest common multiple of 7 and 5 equals :
Multiple of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...
Multiple of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63,...
The lowest common multiple of both 5 and 7 is 35
The the first caller to win both prizes will be the 35th caller
HELP PLS TY ILY BDJXHEJDJ
Answers
Answer:
my guess is the flagpole is 164 in tall
Step-by-step explanation:
if she 60 in tall then her shadow is 36 in taller
the flagpole's shadow is 200in so subtract 36 from 200
find area of trapezoid
Answers
Answer:
150 sqaure ft
Step-by-step explanation:
okay so the formula for area of a trapezoid is
1/2 (b1 + b2) h
so base one of 15 plus two of 10 os 25 ft
25 feet divided by 2 is 12.5 so 12.5 × 12 is 150
If the line of best fit is y = 1.18x 5.4, what is the residual value for the coordinate (5, 12)? 0.3 −0.3 0.7 −0.7
Answers
The residual value for the coordinate from the line of best fit is equal to 0.7 .
The line of best fit is y = 1.18x + 5.4 .
the given point is (5,12)
At x = 5 ,
y = 1.18 × 5 + 5.4
y = 11.3
Residual value = 12 - 11.3 = 0.7
Hence the residual value from the line of best fit is 0.7 .
A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to represent a relationship in a scatter plot with numerous data points. Regression analysis produced it, and it serves as a tool for predicting indicators and price fluctuations.
The eyeball method can be used to roughly build a line of best fit by drawing a straight line on something like a scatter plot and making sure that the total number of points above and below the line is nearly equal (and the line passes through as many points as possible).
To learn more about residual value visit:
https://brainly.com/question/8433351
#SPJ4
The weights of cars passing over a bridge have a mean of 3,550 pounds and standard deviation of 870 pounds.Assume that the weights of the cars passing over the bridge are normally distributed. What is z-score corresponding to a car that weighs 2800 pounds?
Answers
The z-score corresponding to a car that weighs 2800 pounds is approximately -0.86.
We have,
We can find the z-score corresponding to a car that weighs 2800 pounds using the formula:
z = (x - μ) / σ
where x is the weight of the car, μ is the mean weight, and σ is the standard deviation.
Substituting the given values, we get:
z = (2800 - 3550) / 870
z = -0.86
Therefore,
The z-score corresponding to a car that weighs 2800 pounds is approximately -0.86.
Learn more about z-score here:
https://brainly.com/question/15016913
#SPJ1
14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer
Answers
What is extrapolation and why is it a bad idea in regression analysis? O A. Extrapolatio n is the tendency for values of the explanatory variable that are far from the mean to produce values of the response variable that are closer to the may be incorrect if the linear trend does not continue, and so extrapolation generally shoukd not be trusted. mean. B. Extrapolation is prediction far outside the range of the data. These predictions may be incorrect if the linear trend does not continue, and so extrapolation generally should not be trusted. O C. Extrapolation is prediction far outside the range of the data. These predictions may be incorrect if the standard deviation is too large, and so extrapolation generally should not be trusted. Extrapolation is the tendency for values of the explanatory variable that are far from the mean to produce values of the response variable that are closer to the mean. These predictions may be incorrect if the standard deviation is too large, and so extrapolation generally should not be trusted.
Answers
Extrapolation is the act of making predictions or estimations about values of the response variable that lie outside the range of the data used in regression analysis. In simpler terms, it is the process of extending a trend line beyond the range of data in order to predict future outcomes.
Extrapolation is considered a bad idea in regression analysis because it is based on the assumption that the linear trend observed in the data will continue indefinitely. However, this assumption may not always be true, and the further away the prediction is from the range of data, the less accurate the prediction is likely to be. In addition, when extrapolating, there is a greater risk of encountering outliers or extreme values that can skew the prediction. This is because the range of data used in the regression analysis may not fully represent the entire population, and therefore, extrapolation may not provide accurate predictions for the population as a whole.
Therefore, it is important to exercise caution when extrapolating and to be aware of the limitations and potential pitfalls associated with this technique. In general, it is recommended to only make predictions within the range of data used in the regression analysis, and to avoid making predictions too far outside this range.
To know more about Extrapolation visit:
https://brainly.com/question/31964055
#SPJ11
Find y such that the slope between (2, y) and (5, -3) is 7.
Answers
Answer:
y= -24
Step-by-step explanation:
since the slope is 7 the value of y should decrease as the value of x decreases. and since you went back 3 on the x, you should go down 21 on the y resulting in -3-21 which is -24
Help please need anwser
Answers
Answer:
1)55 and for 2) 35
Step-by-step explanation:
All you have to do is and for perimeter.
Simplify the square root of 40x^4
Answers
Answer:
4 = 22
Step-by-step explanation:
Factor 40 into its prime factors
40 = 23 • 5
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
4 = 22
Factors which will remain inside the root are :
10 = 2 • 5
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
2 = 2
At the end of this step the partly simplified SQRT looks like this:
2 • sqrt (10x4)
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x4) = x2
sqrt (40x4) =
2 x2 • sqrt(10)
Simplified Root :
2 x2 • sqrt(10)
PLZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
b
Step-by-step explanation: