(a). Let f(x) = where a and b are constants. Write down the first three 1 + b terms of the Taylor series for f(x) about x = 0. (b) By equating the first three terms of the Taylor series in part (a) with the Taylor series for e* about x = 0, find a and b so that f(x) approximates e as closely as possible near x = 0 (e) (c) Use the Padé approximant to e' to approximate e. Does the Padé approximant overstimate or underestimate the value of e? (d) Use MATLAB to plot the graphs of e* and the Padé approximant to e' on the same axes. Submit your code and graphs. Use your graph to explain why the Pade approximant overstimates or underestimates the value of e. Indicate the error on the graph
Answers
Answer:
(a). Let f(x) = where a and b are constants. Write down the first three 1 + b terms of the Taylor series for f(x) about x = 0.
To find the Taylor series for f(x), we first need to find its derivatives:
f(x) = (1 + ax)/(1 + bx) f'(x) = a(1 + bx) - ab(1 + ax)/(1 + bx)^2 f''(x) = ab(1 - 2ax + b + 2a^2x)/(1+bx)^3 f'''(x) = ab(2a^3 - 6a^2bx + 3ab^2x^2 - 2abx + b^3)/(1+bx)^4
Using these derivatives , we can write the Taylor series for f(x) about x=0:
f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ... = 1 + ax - abx^2 + 2a^2bx^3/3 + ...
Thus , the first three terms of the Taylor series for f(x) about x=0 are:
1 + ax - abx^2
(b) By equating the first three terms of the Taylor series in part (a) with the Taylor series for e* about x = 0 , find a and b so that f(x) approximates e as closely as possible near x = 0 (e)
We have the Taylor series for e* about x=0:
e* = 1 + x + x^2/2! + x^3/3! + ...
Comparing this to the first three terms of the Taylor series for f(x) from part (a), we can equate coefficients to get:
1 = 1 a = 1 -ab/2 = 1/2
Solving for a and b, we get:
a = 1 b = -1
Thus , the function f(x) = (1 + x)/(1 - x) approximates e as closely as possible near x=0.
(c) Use the Padé approximant to e' to approximate e. Does the Padé approximant overestimate or underestimate the value of e?
The Padé approximant to e' is:
e'(x) ≈ (
Explanation:
Related Questions
this is it dont anwser this is for my other account
Answers
Answer:
thanks for the poiunts
Explanation:
When a current carrying coil is placed between the magnetic poles a force acts on it that causes it to rotate what can be done to make the coil rotate faster
Answers
Answer:
increase the field strengthincrease the currentdecrease the moment of inertia of the coilExplanation:
The rotation speed depends on the force applied to the coil, and on the mass (moment of inertia) of the coil. The force can be increased by ...
increasing the magnetic field strength
increasing the coil current
And the moment of inertia can be decreased by ...
making the coil lighter
making the coil more compact.
Any of these changes will increase the rotation speed.
when work that was formerly done by people has been moved to computers, it is said to be ________.
Answers
The term you're looking for is "automated."
When work that was previously performed by humans is now carried out by computers, it is known as automation. This can range from simple tasks like data entry to more complex tasks like decision-making processes. Automation helps to increase productivity and efficiency while also reducing the likelihood of errors and minimizing costs associated with human labor.
Automation refers to the process of transferring tasks, which were previously performed by humans, to computers or machines. This is done to increase efficiency, reduce errors, and save time and resources. Automation can be seen in various industries such as manufacturing, transportation, and customer service.
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explain why clay having been fired
at elevated temperature Loses its
hydroplasticity.
Answers
Firing clay at elevated temperatures causes it to lose its hydro plasticity by removing the water molecules that allow the particles to move and slide past each other. This results in a more rigid and durable material that is suitable for various applications.
What is Clay?Clay is a naturally occurring material composed of fine particles of minerals such as kaolinite, illite, and montmorillonite.
One of the unique properties of clay is its hydroplasticity, which refers to its ability to change shape and form when it comes into contact with water.
When clay is wet, the water molecules fill the spaces between the clay particles, allowing them to slide past each other and become more pliable. This allows the clay to be easily molded into various shapes and forms.
However, when clay is fired at elevated temperatures, the heat causes the water molecules to evaporate, leaving behind a solid mass of mineral particles. The heat also causes the minerals to undergo chemical changes, resulting in the formation of new bonds and the strengthening of existing bonds between the particles.
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The output S/N at thereceiver must be greater than 40 dB. The audio signal has zero mean, maximum amplitude of 1, power of ½ Wand bandwidth of 15 kHz. The power spectral density of white noise N0/2 = 10-10W/Hz and the power loss in the channel is 50 dB. Determine the transmit power required and the bandwidth needed.
Answers
Given that,
The output signal at the receiver must be greater than 40 dB.
Maximum amplitude = 1
Bandwidth = 15 kHz
The power spectral density of white noise is
\(\dfrac{N}{2}=10^{-10}\ W/Hz\)
Power loss in channel= 50 dB
Suppose, Using DSB modulation
We need to calculate the power required
Using formula of power
\(P_{L}_{dB}=10\log(P_{L})\)
Put the value into the formula
\(50=10\log(P_{L})\)
\(P_{L}=10^{5}\ W\)
For DSB modulation,
Figure of merit = 1
We need to calculate the input signal
Using formula of FOM
\(FOM=\dfrac{\dfrac{S_{o}}{N_{o}}}{\dfrac{S_{i}}{N_{i}}}\)
\(1=\dfrac{\dfrac{S_{o}}{N_{o}}}{\dfrac{S_{i}}{N_{i}}}\)
\(\dfrac{S_{i}}{N_{i}W}=\dfrac{S_{o}}{N_{o}}\)
Put the value into the formula
\(\dfrac{S_{i}}{2\times10^{-10}\times15\times10^{3}}<40\ dB\)
\(\dfrac{S_{i}}{30\times10^{-7}}<10^{4}\)
\(S_{i}<30\times10^{-3}\)
\(S_{i}=30\times10^{-3}\)
We need to calculate the transmit power
Using formula of power transmit
\(S_{i}=\dfrac{P_{t}}{P_{L}}\)
\(P_{t}=S_{i}\times P_{L}\)
Put the value into the formula
\(P_{t}=30\times10^{-3}\times10^{5}\)
\(P_{t}=3\ kW\)
We need to calculate the needed bandwidth
Using formula of bandwidth for DSB modulation
\(bandwidth=2W\)
Put the value into the formula
\(bandwidth =2\times15\)
\(bandwidth = 30\ kHz\)
Hence, The transmit power is 3 kW.
The needed bandwidth is 30 kHz.
What are the differences between household and industry
flowmeters?
Answers
Household flowmeters and industry flowmeters differ from each other. The differences between household and industry flowmeters are on the basis of Capacity, Accuracy, Maintenance, Materials, and Purpose.
1. Capacity: Household flowmeters are designed to handle low to medium flows. In contrast, industrial flowmeters are designed to handle a high flow rate.
2. Accuracy: Household flowmeters have lower accuracy compared to industrial flowmeters. This is because household flowmeters are less sensitive to minor changes in flow velocity and pressure.
3. Maintenance: Household flowmeters are easier to maintain than industrial flowmeters. This is because industrial flowmeters have a complex design that requires regular maintenance and calibration.
4. Materials: Industrial flowmeters are built with heavy-duty materials, whereas household flowmeters are built with lightweight materials. This is because industrial flowmeters must withstand harsh operating conditions, whereas household flowmeters operate under normal conditions.
5. Purpose: The purpose of household flowmeters is to measure the flow of liquids and gases in a household. The purpose of industrial flowmeters is to measure the flow of liquids and gases in an industrial setting.
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Which of these construction materials does the government restrict because of toxicity?
A.
lead
B.
silica
C.
concrete
D.
cement
Answers
Answer:
A
Explanation:
It is also a toxic material
Answer:
The correct answer is A. Lead.
Explanation:
I got it right on the Plato test.
a runway identified as runway 27 serves operations oriented to which approximate direction?
Answers
A runway identified as runway 27 serves operations oriented to the westward direction.
What are runways?
A runway is defined as an airport's paved surface. A runway is used for aircraft takeoff and landing operations. The most important runway, without a doubt, is the primary runway, which is the longest runway that has lighting and instrument landing aids. Runways are usually numbered based on their compass bearings, and they are designated L or R if two runways are close together but not parallel. It's worth noting that the numbers don't signify the degree to which the runway is off of a north-south heading, but rather the runway's magnetic bearing.
How to identify the approximate direction of operations from the runway designation?
A runway identified as runway 27 serves operations oriented to the westward direction. The runway numbering system is used to determine the runway direction, which is based on its magnetic direction from 0 to 359 degrees. These numbers are used to designate runway headings in tens, as well as for headings within ten degrees. Runway 27 would be the one with the magnetic heading of approximately 270 degrees (270-279). As a result, an aircraft taking off or landing on runway 27 would travel in an approximately westward direction.
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where the nec does require listing, the equipment shall be installed and used in accordance with the ?
Answers
Where the NEC does require listing, the equipment shall be installed and used in accordance with the listing and labeling conditions specified in the instructions included in the listing or labeling.
In accordance with the listing, equipment should be installed and utilized. A listing is a formal document that lists the criteria and requirements that equipment must meet in order to be deemed safe and functional. A listing implies that an independent third-party organization has tested and validated the equipment to be safe for use. The National Electrical Code (NEC) requires that specific electrical equipment be listed or certified by an independent testing laboratory to ensure that it is safe and suitable for the intended purpose.This ensures that the equipment is properly installed, maintained, and operated for safety and effectiveness.
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Given the binary number 11011011
What is its
Unsigned binary Number ?
Answers
Answer:
219
Explanation:
Unsigned binary number (base two) 1101 1011 converted to decimal system (base ten) positive integer = 219.
Answer:219
Explanation:128+64+16+8+2+1
the two arms of the l-shaped handle on the spigot of (figure 1) have a length ratio of 1:3√. At what angle theta do you want to pull down on the end of the handle to maximize the torque your force causes?30 degree to the left of the vertical line.60 degree to the right of the vertical line. 60 degree to the left of the vertical line. 45 degree to the right of the vertical line. 45 degree to the left of the vertical line. 30 degree to the right of the vertical line.
Answers
The length ratio of the two arms on the l-shaped handle on the spigot in (figure 1) is 1:3. To maximize the torque your force produces 30 degrees to the left of the vertical line, pull down on the end of the handle at an angle theta.
What exactly is the torque?
That force that could enable an element to rotate along an axis is measured as torque. Similar with how force accelerates an item through linear biomechanics, torque accelerates an objects in an orthogonal direction.
What makes the torque significant?
The ability of an engine to manage a load and produce a specific amount of torque needed to rotational the engines on its axis is represented by torque, which is an essential component of generating energy from a car's engine. Each foot (ft) of revolution about a single point, the force is expressed in pounds (lb).
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Why is sand used as a bed for melting of metal in Cupola furnace?
Answers
Answer:
A sand bed is necessary because it provides a refractory bottom for molten metal
:]
If you measure 0.7 V across a diode, the diode is probably made of
Answers
Answer:
Made of Silicon.
Explanation:
A diode is a semiconductor device use in mostly electronic appliances. It is two terminals device consisting of a P-N junction formed either in Germanium or silicon crystal.
Diode can be forward biased or reverse biased.
When a diode is forward biased and the applied voltage is increased from zero, hardly any current flows through the device in the beginning.
It is so because the external voltage is being opposed by the internal barrier voltage whose value is 0.7v for silicon and 0.3v for germanium.
If you measure 0.7 V across a diode, the diode is probably therefore made of Silicon.
NEC 210.11(B) requires that load be evenly proportioned among the different circuits in a panelboard. This is normally performed at the load center panelboard by connecting branch-circuit wiring so that the connected load on the two ____________________ is as equal as possible.
Answers
The National Electrical Code (NEC) provides guidance for safely installing and maintaining electrical systems. NEC 210.11(B) states that the load must be evenly proportioned among the different circuits in a panelboard.
This is usually done at the load center panelboard by connecting branch-circuit wiring so that the connected load on the two poles is as equal as possible.This is because a typical single-phase electrical circuit is a two-wire circuit that includes a hot wire and a neutral wire. A panelboard has multiple branch-circuit breakers that distribute electrical power to the various loads in a building. These breakers are typically arranged in two columns, with one column for each hot wire.
When loads are unevenly distributed across the two hot wires, it can lead to overloaded circuits and overheating. This can result in tripped breakers, damage to equipment, and even fires. To prevent this, the load must be balanced as evenly as possible across both hot wires.One way to achieve this is to connect each load to a separate branch circuit, with each circuit connected to a different hot wire. Another option is to use a three-phase system, which includes three hot wires and a neutral wire.
In this system, the load is distributed across all three hot wires, ensuring that each wire carries an equal load.In conclusion, it is important to ensure that the load is evenly proportioned among the different circuits in a panelboard to prevent overloading and overheating. This can be achieved by connecting branch-circuit wiring so that the connected load on the two poles is as equal as possible.
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Select the correct answer. The most frequent maintenance task for a car is: A. Oil changes B. Tire replacements C. Coolant changes D. Brake replacements
Answers
Answer:
A. Oil changes
Explanation:
It depends on the car and its usage and environment. Usually oil is supposed to be changed every few months, more often if the car is driven a lot. Coolant changes may be indicated as seasons change, so will generally occur less frequently than oil changes.
Tire and brake replacement depend on usage and driving habits. Some owners may never have to replace either one, if they trade their car every year or two. Folks who drive with their foot on the brake pedal may have to replace brakes relatively often.
The most frequent task is generally oil changes.
Answer:
A. Oil changesthe most frequent maintenance task for a carYour new team is working hard, but they are all less experienced than you and don't complete their tasks as quickly.What would you be most and least likely to do? (A). Reach out to your manager to discuss the situation.Try to identify the best way to support the new associates. (B).Remind your coworkers of performance expectations and that they need to be working harder to complete tasks. (C). Offer to help others complete their tasks; observe their work process and provide some tips that might help them. (D). Give your coworkers more time to figure out how to do the task; they likely just need more practice with what they've already learned.
Answers
The only difference between all GMA welding machines and some FCA welding machines is that all GMA welding machines must have a ______________.
Answers
Answer: Shielding gas solenoid
Explanation:
How do traffic lights involve science??
Answers
Answer:
Many would pair the engineering and science behind it together. The sensor requires have a detective system for when cars pass by. It can also cycle the lights (change from red, green, and yellow). Traffic can flow uninterrupted on the main road. So, science is an important part.
Ideally speaking, bonds tend to form between two particles such that they are separated by a distance where force is exerted on them, and their overall energy is:________
a. a negative, minimized
b. a positive, minimized
c. zero, minimized
d. zero, maximized
e. a positive, maximized
f. a negative, maximized
Answers
Answer:
a g i
Explanation:
nnj
Discuss in detail the manners of interaction with opposite gender
Answers
Answer:
8 Tips on Better Communication with the Opposite Sex
Put emotions away. Ladies, this one is more aimed at us, for the most part. ...
Forget your pride. In discussions, especially these days, people always want to be the one that prevails. .
Put yourself in their shoes. .
Listen. ...
Respond. ...
Actually communicate. ...
Be detailed. ...
Don't communicate too much.
Explanation:
Type the correct answer in the box. Spell all words correctly.
A genetically engineered hormone, , can treat Mary’s child for growth hormone deficiencies by stimulating body growth and increasing muscle mass.
Answers
Answer:
recombinant human growth
Explanation:
Answer:
recombinant human growth
Explanation:
yes
The roller coaster car having a mass m is released from rest at point A Neglect friction (Figure 1) Part A
It the track is to be designer so that car does not leave it at B determine the required height h Express your answer to three Significant figures and Include the appropriate units. Part B
Find the speed of the car when it roaches point C. Express your answer to three significant figures and include the appropriate units.
Answers
The car's speed as it approaches the spot Part B's v = 14.3 m/s and Part A's h = 8.94 metres.
What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar quantity. The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. The average speed of an item in a period of time is the distance travelled by the object divided by the duration of the period. Velocity and speed are not the same thing.
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which professional uses practical knowledge of science to design and manufacture machines? engineer experimental scientist technician theoretical scientist
Answers
Engineers - professionals who apply scientific knowledge to design and manufacture machines.
We have,
Engineers are professionals who use their practical knowledge of science, mathematics, and technology to design, develop, and manufacture machines, systems, and structures.
They apply scientific principles and theories to create practical solutions for various industries and sectors.
Engineers utilize their expertise to design, analyze, and improve machines, ensuring they meet specific requirements, functionality, safety standards, and efficiency.
They consider factors such as materials, cost-effectiveness, environmental impact, and feasibility while designing and manufacturing machines.
Overall, engineers combine scientific knowledge with practical skills to innovate and create technology and machinery that serves various purposes in society.
Thus,
Engineers - professionals who apply scientific knowledge to design and manufacture machines.
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List the five lines that include short dashes.
Answers
Answer:
OBJECTLINE
HIDDEN LINE
SECTION LINE
CENTER LINE
Explanation:
What is the impact on fuel economy when using E85 instead of gasoline?
Answers
Answer:
energy security ethanol
True or False: Conditions, like the number of times repeated, are used to end a [Repeat] block.
Answers
Answer:
True. needa type in 20 more letters
Explanation:
ye.
procedure for replacing wheel cylinder seals
Answers
Before we go into the specifics of the brake job, you should be aware that wheel cylinders are always replaced in pairs, even if one is trouble-free.
What is wheel cylinder?A part of a hydraulic drum braking system is a wheel cylinder. It is a part of every wheel and is often found above the shoes at the top of the wheel.
Its purpose is to apply pressure to the shoes in order to bring them into contact with the drum and cause friction to stop the vehicle.
The Wheel Cylinder applies pressure to the brake shoes in a drum brake system, and the brake shoes' contact with the drum causes the vehicle to slow down and come to a stop.
At the drum brake, raise the car. In the owner's manual, find the drum brake section.Examine your brake seals. Find the brake seals in the owner's manual for your car. Verify whether they are worn out or damaged visually.Remove the brake wheel, step 3.Thus, this can be the procedure to change the wheel cylinder seal.
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Drag each tile to the correct box. Not all tiles will be used.
Adam wants to become a certified professional engineer. What are the steps that he will have to follow?
Answers
Answer:
I think it is the 2,3,5 and 1 ones
(250-68(B)) The connections (attachment) of the grounding electrode conductor to a grounding electrode shall be made in a manner that will ensure a permanent and effective _____.
Answers
The connections (attachment) of the grounding electrode conductor to a grounding electrode shall be made in a manner that will ensure a permanent and effective electrical connection.
An electrode is a conductor that is used to establish electrical contact with a non-metallic part of a circuit, such as a semiconductor or an electrolyte. Electrodes are commonly used in many fields, including electronics, electrochemistry, medical devices, and industrial applications.
In electronic devices, electrodes are used to connect electrical circuits to components such as transistors, diodes, and capacitors. In electrochemistry, electrodes are used to initiate and conduct electrochemical reactions, such as in batteries or electroplating.
Different types of electrodes may be used for different applications, including metal electrodes, carbon electrodes, and semiconductor electrodes. Electrodes may also be coated with different materials to enhance their properties, such as platinum or gold to improve conductivity, or to make them more chemically resistant.
Overall, electrodes play a critical role in enabling electrical and electrochemical processes in a wide range of applications.
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What song do you play most often?
What’s your favorite quote from a movie?
What’s your “go to” joke?
Answers
Answer:
I play dynamite BTS.
”Don’t give up!”
Knock knock who’s there jimmy, jimmy who jimmy back my formula!
Explanation: Thx for asking
.
Answer:
1: I listen to a lot of different types of songs but one I play a lot is "Chasing" by NF
2: I don't really know but... Probably, " There's a snake in my b0ot!" lol
3: My "go to" joke is 100% always ... " If I look like my mom, would I technically be my dads t y p e?"
It gets them every time. ;)
