The actual error when the first derivative of f(x) = x - 21n x at x = 2 is approximated by the following formula with h = 0.5: - 3f(x) - 4f(x - h) + f(x - 2h) f'(x) = 12h Is: 0.00475 0.00142 0.00237 0.01414
Answers
The actual error when approximating the first derivative is approximately 0.00237.So, the correct answer is option c. 0.00237.
To calculate the actual error when approximating the first derivative of \(f(x) = x - 2ln(x)\) at x = 2 using the given formula with h = 0.5, we need to compare it with the exact value of the derivative at x = 2.
First, let's calculate the exact value of the derivative:
\(f'(x) = d/dx (x - 2ln(x)) = 1 - 2/x\)
Substituting x = 2:
\(f'(2) = 1 - 2/2 = 1 - 1 = 0\)
Now, let's calculate the approximate value of the derivative using the given formula:
\(f'(2)=\frac{3f(2) - 4f(1.5) + f(1)}{12h}\)
Substituting \(f(2) = 2 - 2ln(2)\), \(f(1.5) = 1.5 - 2ln(1.5)\), and\(f(1) = 1 - 2ln(1)\):
\(f'(2) = \frac{3(2 - 2ln(2)) - 4(1.5 - 2ln(1.5)) + (1 - 2ln(1))}{12(0.5)}\)
\(f'(2)= \frac{6 - 6ln(2) - 6 + 8ln(1.5) + 1 - 0}{6}\)
\(f'(2)= \frac{1 - 6ln(2) + 8ln(1.5)}{6}\)
Now, we can calculate the actual error:
Error = \(|f'(2) - f'(2)|\) = \(|(1 - 6ln(2) + 8ln(1.5))/(6) - 0|\) = \(|(1 - 6ln(2) + 8ln(1.5))/(6)|\)
Calculating this expression gives:
Error ≈ 0.00237
Therefore, the actual error when approximating the first derivative is approximately 0.00237. Therefore, the correct answer is option c. 0.00237.
The question should be:
The actual error when the first derivative of f(x) = x - 2ln x at x = 2 is approximated by the following formula with h = 0.5:
\(f'(x)= \frac{3f(x)-4 f(x-h)+f(x-2h)}{12h} is\)
a. 0.00475
b. 0.00142
c. 0.00237
d. 0.01414
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Related Questions
The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
Answers
The graphical representation that would be most appropriate for the data, given the number of different breakfast cereals sold, is,
B. Histogram, because there is a large set of data.
Since, We know that;
Histograms are used for large sets of data because they provide a visual representation of the distribution of the data. They are particularly useful for understanding the distribution of continuous variables, such as measurements or time series data.
One of the main advantages of histograms is that they allow for easy comparison of large sets of data. The use of bars to represent the data makes it easy to see the overall shape of the distribution and identify patterns or outliers. Additionally, histograms can be used to compare multiple sets of data at once, allowing for easy comparison of different groups or changes over time.
Another advantage of histograms is that they can be used to identify the underlying probability distribution of a dataset, which is useful for statistical analysis and modeling.
This is why, given the fact that the data contains information from 1, 000 different cereals, a histogram is best to show this as the data is large.
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Divide using any method 2x^2+5x+1 ÷ X+3
Answers
Question:
Solve the equation 2x2−5x+3=0 by the method of completing square.
Answer:
We have,
2x2−5x+3=0
⇒x2−25x+23=0 (Dividing throughough by 2)
⇒x2−25x=−23 (Shifting the constant term on RHS)
⇒x2−2(45)x+(45)2=(45)2−23 (Adding (21Coeff.ofx)2 onboth sides)
⇒(x−45)2=1625−23⇒(x−45)2=16
help me with this PLACE
Draw a quadrilateral that has two 60 degree angles and two 120 degree angles.
Answers
Answer:
Step-by-step explanation:
Draw a straight line.
Then draw 2 lines of equal length from the 2 ends of the line at angles of 120 degrees going up and apart.
Then draw the fourth line joining the ends of these 2 lines.
The 2 angles formed will equal 60 degrees.
The quadrilateral formed is a trapezoid.
HELP ASAP PLEASE OMG PLEASE HELP ME
Answers
Answer:
AB = 4
\(m\angle E=30^\circ\)
Step-by-step explanation:
Similar shapes
Two figures are similar if the ratios of the lengths of their corresponding sides are equal. The corresponding angles are also congruent.
Being ABCD and EFGH similar, the ratio of the lengths of AB and EF is equal to the ratio of the lengths of AD and EH, thus:
\(\displaystyle \frac{AB}{EF}=\frac{AD}{EH}\)
Solving for AB:
\(\displaystyle AB=\frac{AD}{EH}\cdot EF\)
Since AD=6, EH=1.5, and EF=1:
\(\displaystyle AB=\frac{6}{1.5}\cdot 1\)
AB = 4
Since angle A is congruent to angle E:
\(m\angle E=m\angle A\)
\(\mathbf{m\angle E=30^\circ}\)
Which expression is equivalent to x2(3x3−2x)−(−7x3+2) ?
Answers
Answer:
R27.
Step-by-step explanation:
Graph y = 2x and y= 2x
What x-values are solutions to the system?
Answers
Answer:
Wait u gave the same equation twice, do u mind checking back to it?
Step-by-step explanation:
...yea i just need help (:
Answers
Answer:
2/3-4
3 1/3
-1*3.3=-3.3
-3 1/3 divided by 5/6
-4
so a
Hope This Helps!!!
Answer:
-2/3+4÷5/6
-2+12÷3÷5/6
10/3÷5/6
10/3x6/5
2/1x2/1
4/1
4
Step-by-step explanation:
hope this is helpful
The oscillating current in an electrical circuit is as follows, where I is measured in amperes and t is measured in seconds. I = 3 sin(120nt) + cos(60nt) Find the average current for each time interval
Answers
To find the average current for each time interval in the given oscillating current equation, integrate the function over the interval and divide by its length. This average current represents the steady component of the oscillating current.
To find the average current for each time interval in the given oscillating current equation I = 3 sin(120nt) + cos(60nt), we need to calculate the average value of the current over specific time intervals.
The average value of a function over a time interval is obtained by integrating the function over that interval and dividing by the length of the interval.
Let's consider the time interval from t = 0 to t = T, where T is the period of the current waveform. In this case, the period can be found by taking the reciprocal of the frequency, so T = 1/f, where f is the frequency.
To find the average current over this time interval, we integrate the current function I = 3 sin(120nt) + cos(60nt) from t = 0 to t = T, and then divide by T. The integral of sin(120nt) and cos(60nt) can be evaluated using standard trigonometric integral formulas.
Once we have the value of the integral over the time interval, we divide it by T to find the average current.
We can repeat this process for different time intervals to find the average current for each interval of interest.
It's important to note that the average current represents the steady component of the oscillating current, which is the value that would produce the same amount of power in a resistive element.
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A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?
Answers
Answer:
son2: 5
son1: 10
Step-by-step explanation:
2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59
3x = 15
x = 5
The age of each boy at present will be 2 years and 3 years.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the age of the sons will be x and y.
A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be
x = 2y
In 3 years, the sum of all their ages will be 59 years. Then the equation will be
x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59
Simplify the equation, we have
3x + 3y + 41 = 59
6y + 3y = 59 – 41
9y = 18
y = 2
Then the value of x will be
x = 2y
x = 2(2)
x = 4
Thus, the age of each boy at present will be 2 years and 3 years.
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Evaluate these quantities. a) −17 mod 2 b) 144 mod 7 c) −101 mod 13 d) 199 mod 19
Answers
The evaluated quantities are:
a) −17 mod 2 = -1
b) 144 mod 7 = 4
c) −101 mod 13 = -10
d) 199 mod 19 = 9
To evaluate the given quantities, we will calculate the remainder when the given numbers are divided by the divisor.
a) −17 mod 2:
To find −17 mod 2, we divide −17 by 2 and calculate the remainder:
−17 ÷ 2 = -8 remainder -1
Therefore, −17 mod 2 is -1.
b) 144 mod 7:
To find 144 mod 7, we divide 144 by 7 and calculate the remainder:
144 ÷ 7 = 20 remainder 4
Therefore, 144 mod 7 is 4.
c) −101 mod 13:
To find −101 mod 13, we divide −101 by 13 and calculate the remainder:
−101 ÷ 13 = -7 remainder -10
Therefore, −101 mod 13 is -10.
d) 199 mod 19:
To find 199 mod 19, we divide 199 by 19 and calculate the remainder:
199 ÷ 19 = 10 remainder 9
Therefore, 199 mod 19 is 9.
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7) What does a multiplier of \( 1.2 \) mean?
Answers
A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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I know its 0=0 but can someone tell me which one between the two.
Answers
Answer:
The first one
Step-by-step explanation:
the two sides cancel each other out
Combine the terms to simplify the expression: 5y+12x-y-8x
Answers
Answer: 5y + 4x
Step-by-step explanation:
Answer:
4y+4x
Step-by-step explanation:
5y+12x-y-8x
-y -8x
4y+4x
Many people enjoy cross-country and downhill skiing for recreation and for exercise. For others, skiing is a competitive sport. In ski races, fractions of a second can make the difference between winning and finishing second. Describe how the skier’s velocity changes during the race
Answers
The skier's velocity changes during the race due to the force of gravity, making turns on the course, and the conditions of the snow and terrain.
The skier's velocity changes during the race in several ways. Firstly, the skier starts at a slower velocity and gradually accelerates as they move down the slope. This is due to the force of gravity pulling them downwards, which increases their speed.
Secondly, the skier's velocity changes as they make turns on the course. When making a turn, the skier's velocity decreases as they have to slow down in order to make the turn. Once they have completed the turn, their velocity increases again as they accelerate down the slope.
Lastly, the skier's velocity also changes due to the conditions of the snow and the terrain. For example, if the snow is packed and icy, the skier's velocity will be faster than if the snow is soft and powdery. Similarly, if the terrain is steep, the skier's velocity will be faster than if the terrain is flat.
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Please help.
Is algebra.
Answers
Explanation because I’m to dum to get a answer right by my self so I got it from an app .
Write expressions for the perimeter and the area of this algebra tile shape. Then simplify each expression by combining like terms.
Answers
The given algebra tile shape can be divided into two rectangles and a square with the side length of 1 unit each.
Let the side length of the square be 'x'. The length of the horizontal rectangle is (2 + x) units, and the length of the vertical rectangle is (1 + x) units.
Now,
Perimeter of the given shape = Sum of the length of all the sides,
(2 + x) + (1 + x) + (2 + x) + (1 + x) + 4= 6 + 4x,
Area of the given shape = Area of the square + Area of the vertical rectangle + Area of the horizontal rectangle
x² + x(1 + x) + x(2 + x)= x² + 3x + x²= 2x² + 3x
Thus, the expressions for the perimeter and the area of the given algebra tile shape are
6 + 4x and 2x² + 3x,
respectively .Simplifying each expression by combining like terms,Perimeter of the given shape
= 6 + 4x= 2(3) + 2(2x)= 2(2x + 3)Area of the given shape = 2x² + 3x= x(2x + 3)Hence, the simplified expressions for the perimeter and the area of the given algebra tile shape are 2(2x + 3) and x(2x + 3), respectively.
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Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the standard deviation for the number of cells infected was 80 and the mean was 350. What is the standard error
Answers
Thus, standard error for this sample of tissue cells infected in a laboratory treatment is 5.33.
The standard error (SE) is a measure of how much the sample mean deviates from the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
In this case, the sample size is 225, the standard deviation is 80, and the mean is 350. Therefore, the standard error can be calculated as follows:
SE = 80 / √(225)
SE = 80 / 15
SE = 5.33
The standard error for this sample of tissue cells infected in a laboratory treatment is 5.33. This means that the sample mean of 350 is likely to be within 5.33 units of the population mean.
The smaller the standard error, the more precise the estimate of the population mean. In this case, the standard error is relatively small compared to the standard deviation, which suggests that the sample mean is a relatively accurate estimate of the population mean.
However, it is important to note that the standard error only provides information about the precision of the estimate, not its accuracy. Other factors, such as sampling bias or measurement error, could still affect the accuracy of the estimate.
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Given that 3 * 6 = 12 and 2 * 5 = 9, then a * b may be defined as
Answers
Answer:
3 *6=12
3+6=9
9+3=12
2*5=2+5=7
7+2=9
a*b=a+b+a
please help me rn!!!!!!!!
Answers
Answer:
A B and C
Step-by-step explanation:
it's a simple question
what is 9x2y-3 if x = 5 and y = 3.
Answers
Answer:
267
Step-by-step explanation:
im running out of things to say
Answers
Answer:
i think its b
Step-by-step explanation:
how do i use the quadratic formula on 5x + x2 + 10 = 0
Answers
Answer:math away is the best for the question u have
Step-by-step explanation:
Mathaway
Step-by-step explanation:
Solve the equation for x by finding a, b and c o f the quadratic then applying the quadratic formula.
5 ± i√15
x = ----------------------------
2
A triangle has vertices at A (−2, −2), B (−1, 1), and C (3, 2). Which of the following transformations produces an image with vertices A′ (−2, 2), B′ (−1, −1), and C′ (3, −2)?
Answers
Kelly was building a bed for her dollhouse. She used her bed, which is 4 feet × 6 feet, as a guide. She scaled down the dimensions of her bed by a factor 1 over 5 . What are the dimensions of the model bed she built?
0.8 foot × 1.2 feet
0.4 foot × 0.6 foot
0.08 foot × 0.12 foot
0.04 foot × 0.06 foot
Answers
Answer:
The first one
Step-by-step explanation:
1/5 =0.20
0.20 * 4 = 0.8 feet
0.20 * 6 = 1.2 feet
How many lines of symmetry does the figure below have?
A) 0
B) 1
C) 2
D) 3
Answers
What is the decimal multiplier to decrease by 78%?
Answers
Answer:
0.22
Step-by-step explanation:
Let assume the number to be reduced be 100
Reducing it by 78% will be:
100 - ( 78% of 100 )
100 - (78/100)×100
100 - 0.78 × 100
100 - 78 = 22
Since the answer is 22. Hence,
22/100 will be the multiplier
0.22 × 100 = 22
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Step-by-step explanation:
Which is the best reason why 2/5 is the exact quotient for 1/4÷ 5/8 ?
Answers
Answer:
2/5.
Step-by-step explanation:
1/4 / 5/8
= 1/4 * 8/5
= 1*8 / 4*5
= 8/20
= 2/5.
Solve 3(x - 2) < 18
Answers
Hi there!
\(\large\boxed{x < 8}\)
3(x - 2) < 18
Begin by dividing both sides by 3:
3(x - 2)/3 < 18/3
x - 2 < 6
Add 2 to both sides:
x - 2 + 2 < 6 + 2
x < 8
x< 8
Hope this is the answer you are looing for.
Which of the following describes the graph of y-√√-4x-36 compared to the parent square root function?
stretched by a factor of 2, reflected over the x-axis, and translated 9 units right
stretched by a factor of 2, reflected over the x-axis, and translated 9 units left
stretched by a factor of 2, reflected over the y-axis, and translated 9 units right
stretched by a factor of 2, reflected over the y-axis, and translated 9 units left
Save and Exit
Next
Submit
Answers
The statement that describes the graph of y-√√-4x-36 compared to the parent square root function is: d. stretched by a factor of 2, reflected over the y-axis, and translated 9 units left
What is graph?Stretch by a factor of 2: Multiply the input of the function by 2. The new function is f(2x).
Reflect over the y-axis: Negate the output of the function. The new function is -f(2x).
Translate 9 units left: Subtract 9 from the input of the function. The new function is -f(2x - 9). So if you have an original function f(x) the transformed function would be -f(2x - 9).
Therefore the correct option is d.
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A hospital stores one type of medicine in 222-decagram containers. Based on the information given in the box above, how many 111-milligram doses are there in one 222-decagram container?
Answers
Answer:
2,220,000 mlg
Step-by-step explanation:
This question can be solved by a simple conversion calculation. Thankfully we're converting between two units of measurement with the same base!
So First, let's convert 222 decagrams to grams, and then convert grams to milligrams.
The conversion rates we need are:
1 decagram = 10 grams
1 gram = 1000 milligrams
Now for the math!
\(222 dg *\frac{10g}{1dg} =2220g\\then...2220g * \frac{1000mlg}/1g\\\\\\=2,220,000 mlg\)