If f(x)=ex and the 4th degree Taylor polynomial of f(x) centered at 2, what is T4(2.4)?
Round your answer to four decimals.
Answers
The fourth degree Taylor polynomial of f(x) centered at 2 the \(T_4(2.4) = 11.0225\).
What is Taylor polynomial?
The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.
Given:
\(f(x) = e^x\) centered at 2.
\(f(2) = e^2\)
\(f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2\)
Therefore,
\(T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225\)
Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the \(T_4(2.4) = 11.0225\).
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Related Questions
Select the correct answer from each drop-down menu. Each graph shows the results of a transformation applied to function f where f(x) = (1/2)^x.
Complete the statement given that g(x) =f(kx). The graph of function g is graph Because the graph a function g is the result of a  applied to the graph of function F .
Answers
Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.
What is a graph?A graph can be described as a pictorial representation or a diagram that represents data or values in an organized manner.
The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.
In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.
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please help I will mark BRAINLIEST
Answers
Answer:
Your answer is t>28
Have a nice day!
mark as brainliest
Answer:
T>28
Step-by-step explanation:
What is the area of the triangle shown?
Answers
Answer:
you need to show the triangle shown on your math question or we can't answer it
Step-by-step explanation:
Leonardo tiene que colocar una malla, para facilitar la tarea utilizó un plano del terreno de su rancho y lo seccionó como un plano cartesiano. Para instalar la malla debe utilizar 5 postes que se deben colocar a la misma distancia de separación uno de otro. Observa que el primer poste deberá de ser colocado en la coordenada (-4, -6) y el último en la coordenada (-0, 2) ¿en qué coordenadas deberá colocar los 3 postes restantes?, ¿qué procedimiento utilizaste para ubicar los tres postes faltantes?
Answers
Answer:
Es una pregunta doble, calcule una y grafíquela, calcule la otra y grafíquela, ps: dame lo más inteligente.
Pls help with math asap
Answers
X = 17
\( \large{ \text{Hi, Hope you are fine!}}\)
GIVEN:\( \bull \: \: \: \sf{\angle CGE= x \degree}\)
\( \bull \: \: \: \sf{ \angle AGF = 75 \degree}\)
\( \bull \: \: \: \sf{AGC=90 \degree}\)
TO FIND:\( \bull \: \: \: \sf{Value \: of \: x}\)
SOLUTION:
\( \sf{\angle AGC + \angle AGD=180° (Linear \: pair)}\)
\( \sf{:\implies90 \degree+ \angle AGD=180° }\)
\( \sf{ :\implies\angle AGD=180° - 90 \degree}\)
\( \sf{:\implies \angle AGD= 90 \degree}\)
\( \sf{:\implies\angle FGD= \angle CGE=x}\)
[Vertically opposite angle]
\( \sf{ \angle AGD= 90 \degree}\)
\( \sf{:\implies \angle AGF+ \angle FGD= 90 \degree}\)
\( \sf{ :\implies75 \degree + x = 90 \degree}\)
\( \sf{ :\implies x = 90 \degree - 75 \degree}\)
\( \sf{ :\implies \: x = 15 \degree}\)
Consider a medium with parameters € = 1.2 (10^-10 )F/m , n= 3(10^-3) H/m and sigma=0. Magnetic field intensity in the medium is given as R = 2cos (10^10t- 600x)äz Am.
Use Maxwell's equations to obtain the followings:
1) Magnetic flux density
These questions is circuit theory
Answers
Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:
\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),
where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).
In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:
\(\displaystyle \nabla \times \mathbf{H} =0\).
Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):
\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).
Using the curl identity and applying the chain rule, we can expand the expression:
\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:
\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Differentiating the cosine function with respect to \(\displaystyle x\):
\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).
Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):
\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).
Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:
\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).
Simplifying the equation:
\(\displaystyle \sin( 10^{10} t-600x) =0\).
The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):
\(\displaystyle 10^{10} t-600x =n\pi\),
where \(\displaystyle n\) is an integer. Rearranging the equation:
\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).
The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.
Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.
Thus, the correct expression for the magnetic flux density in the given medium is:
\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).
WILL GIVE BRAINLIEST
Answers
Answer: x = 28
Step-by-step explanation:
Trust me :)
5 A triangle has a base length of 2x cm and a height of (x - 3) cm. If its area
is 18 cm², calculate its height and base length.
Answers
Answer:
base = 12; height = 3
Step-by-step explanation:
Area: ( b x h ) / 2
base: 2x
height: (x - 3)
---------------------------------
( ( 2x )*( x - 3 ) )/ 2 = 18
( 2x ^2 - 6x ) = 36
2x ^2 - 6x - 36 = 0
(quadratic formula)
x = 6
x = -3
---------------------------------
taking the positive value : x = 6
---------------------------------
base: 2x = 2(6) = 12
height: x - 3 = 6 - 3 = 3
Using order of operations how would you solve (3+4)-9 with an equation!!
Answers
(7)-9= -54
Which statements are true about polygons? Select three options. All sides and all angles in a polygon are congruent. The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. In a polygon, all segments with a common endpoint are collinear. If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon. The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.
Answers
Answer:
B, D, E
Step-by-step explanation:
Just took test :D
A polygon refers to a flat or two-dimensional shape which is closed and has straight sides. A polygon doesn't curved sides.
From the options given, the true statements about polygons include:
• The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.
• If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon.
• The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.
Therefore, the correct options are B, D and E.
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Consider the geometric below:
1 8 27
3.1.1. Determine the number of cubes in the 5th term 3.1.2. Draw the 6th term.
Answers
The number of cubes in the 5th term is 125
How to determine the number of cubes in the 5th termFrom the question, we have the following parameters that can be used in our computation:
The sequence of cubes
In the above sequence, we can see that the term is raised to the power of 3 to get the new term
This means that
The nth term is then represented as
f(n) = n³
For the 5th cube, we have
n = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 5³ = 125
Hence, the number of cubes in the 5th term is 125
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
Answers
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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The graph below shows the line y=[x]. If the line y=|x|*2 were graphed on the same grid, hc would it compare to the line shown in the graph below.
Answers
The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.
How to identify the transformation?The functions for this problem are defined as follows:
Parent function: y = |x|.Transformed function: y = 2|x|.When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.
Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.
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What is the rate if change for y = x - 4
Answers
Answer:
The rate of change is 1
Step-by-step explanation:
This is because the slope is x, and -4 is just the y-intercept, which has nothing to do with the slope. Because the slope is x, that means that it is positive 1.
Answer:
Rate of Change = 1
Step-by-step explanation:
Rate of Change = Slope = m
y = mx + b
y = (1)x -4
m = 1
() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answers
Answer:
Step-by-step explanation:
Identify the angle relationship pair for each angle below and explain how you know
Answers
4)they are congruent bc the vertical angle theorem
hope this helps!
What is the mode of the following data values?
54, 78, 16, 26, 16
O A. 26
O B. 38
O C. 16
O D. 48
Answers
Answer: C. 16
Step-by-step explanation:
The mode represents the most frequently occurring value in a data set. A data set may have more than one mode. It is one of the measures of central tendency.
Answer:
C
Step-by-step explanation:
because in the given data the number which is 16 is repeated twice so it means it is the mode. Because when we say mode it is the most used number im the given date
Ruth wants to find the decimal equivalent of 226
, so she divides. Study Ruth’s work shown here, and then answer the questions below.
Answers
The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,
What is a rational number?A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).
We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:
22/6 = 3.666666...
We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.
Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.
The difference between 40 and the product of these digits and 6 is always 4.
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5,11,18,1,4,?,16,49,121
What is the value of the question mark
Answers
Answer:
8
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Split into groups of 3.
5, 11, 18
1, 4, ?
16, 49, 121
(5 − 1)² = 16
(11 − 4)² = 49
(18 − ?)² = 121
Therefore, ? = 7.
wat is 24,12,6 to the 8th term. Round it to the nearest 1000
Answers
We can see that 24 divided by 2 is 12. Similarly, 12/2 is 6 and so on. Then, the sequence rule can be written as
\(a_n=24(\frac{1}{2})^{n-1}_{}\)For instance,
\(\begin{gathered} a_1=24(\frac{1}{2})^{1-1}=24(\frac{1}{2})^0=24\times1=24 \\ a_2=24(\frac{1}{2})^{2-1}=24(\frac{1}{2})=12 \\ a_3=24(\frac{1}{2})^{3-1}=24(\frac{1}{4})=6 \end{gathered}\)Then, by substituting n=8 (8th term) into the first equation, we have
\(a_8=24(\frac{1}{2})^{8-1}=24(\frac{1}{2})^7=24\times\frac{1}{128}=0.1875\)therefore, by rounding to the nearest thousandth, the answer is 0.188.
What is 10% of 800Hhhhhhhhhhhh
Answers
find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
Answers
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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Eliana knit a total of 328 centimeters of scarf over 8 nights. How many nights will Eliana have to spend knitting in order to knit a total of 1,845 centimeters of scarf? Assume the relationship is directly proportional.
Answers
We can write a proportion to help us solve
328 cm 1845 cm
--------------- = ----------------
8 nights x nights
Using cross products
328 * x = 1845 *8
328x =14760
Divide each side by 328
328x/328 = 14760/8
x =45
It will take 45 nights
Find the total surface area of the solid below. Round your answer to the nearest tenth.
x= 11.6, y = 6.3, and z = 15.5
Answers
Answer:
494.16 units²
Step-by-step explanation:
Total surface area of the solid = 4(area of a triangular face) + area of the square base
Area of a triangular face = ½*b*h
b = x = 11.6
h = z = 15.5
Area = ½*11.6*15.5 = 89.9 units²
Area of the four triangular faces = 4(89.9) = 359.6 units²
Area of the square base = s²
s = x = 11.6
Area = 11.6²
Area = 134.56 units²
✔️Total surface area of the solid = 359.6 + 134.56 = 494.16 units²
(3х +20) (5х – 16)
Find x
Answers
Answer:
x=18?
Step-by-step explanation:
oops if its expanding brackets x doesnt equal to 18
Answer:
The Value Of X Is 15x^2+52 hope it helps u
how would I find the area and perimeter
Answers
The little lines through the 4 sides mean all the sides are the same length.
The area is side x side = 8 x 8 = 64 square cm.
Perimeter is the sum of the 4 sides = 8 + 8 + 8 +8 = 32 cm.
Answer:
Perimeter
P =a+a+a+a =4a
P = 4*8
P=32cm
Area
A = a*a = \(a^{2}\)
A = \(8^{2}\)
A = 64\(cm^{2}\)
A house is sold for $195,000. The mortgage is $168,745.60 at 8%. Annual taxes are $3,893.25. The closing will occur on June 15. What are the total prorations for interest (for the full month) and for property taxes to the nearest $100? Will the prorations be added to, or subtracted from, the seller's equity?
Answers
The total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
To calculate the total prorations for interest and property taxes, we need to determine how much the seller owes for each of these expenses up to the closing date of June 15.
First, let's calculate the daily interest rate on the mortgage. We can do this by multiplying the principal amount of the mortgage ($168,745.60) by the annual interest rate (8%) and then dividing by 365 (the number of days in a year):
Daily interest rate = ($168,745.60 x 0.08) / 365 = $36.94
Next, we need to determine the number of days from the start of the month (June 1) to the closing date (June 15):
Number of days = 15 - 1 = 14
Using the daily interest rate and the number of days, we can calculate the proration for interest:
Proration for interest = ($36.94 x 14) = $516.76
To calculate the proration for property taxes, we need to divide the annual property taxes ($3,893.25) by 365 to get the daily property tax rate:
Daily property tax rate = $3,893.25 / 365 = $10.65
Next, we need to determine the number of days from the start of the year to the closing date (June 15):
Number of days = 165
Using the daily property tax rate and the number of days, we can calculate the proration for property taxes:
Proration for property taxes = ($10.65 x 165) = $1,754.25
Therefore, the total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
These prorations will be subtracted from the seller's equity, since they are expenses that the seller owes up to the closing date.
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4. the cost of 5 CDs and a $12 DVD
Answers
Answer:
42
Step-by-step explanation:
Assuming CDS are half of DVDs, the answer would be 30 + 12
prove that, given a nonnegative integer , there is a unique nonnegative integer such that m^2 < sqrt n < (m 1)^2
Answers
It is proved that m = √n.
To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:
m^2 ≤ n < (m + 1)^2.
So, after taking the square root, it will be:
m ≤ √n < m + 1
From that we can see m = √n is the unique m.
What is a nonnegative integer?A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.
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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.
4% as a fraction or mixed number in simplest form
Answers
Answer:
1 /25
Step-by-step explanation:
percent means
out of 100
⇒
4
%
=
4
100
as a fraction
To simplify the fraction we require to find a
common factor
to both 4 and 100 and reduce the fraction by dividing. The common factors are 2 and 4 . Choose the largest, that is 4
⇒
4
100
=
4
÷
4
100
÷
4
=
1
25
This calculation is usually set out using
cancelling
4
100
=
4
1
100
25
=
1
25
←
in simplest form
A fraction is in
simplest form
when no other factor but 1 will divide into the numerator/denominator.