Antiderivative is a fundamental concept in calculus. It refers to finding a function that, when differentiated, results in a given function. In other words, if F(x) is an antiderivative of f(x), then F'(x) = f(x). It is also known as the indefinite integral.
A.) The antiderivative of f(t) = [tex]e^{7t}[/tex] is given by F(t) = (1/7)[tex]e^{7t}[/tex] + C, where C is the constant of integration. This is because the derivative of (1/7[tex]e^{7t}[/tex] + C is (1/7)[tex]e^{7t}[/tex].
B.) The antiderivative of f(z) = 2019 is given by F(z) = 2019z + C, where C is the constant of integration. This is because the derivative of 2019z + C is 2019.
C.) The antiderivative of f(x) = 2x + e is given by F(x) = x² + ex + C, where C is the constant of integration. This is because the derivative of x² + ex + C is 2x + e.
D.) The most general form of the antiderivative of f(x) = [tex]xe ^ {x^2[/tex] is F(x) = (1/2) [tex]e^{x^2[/tex] + C, where C is the constant of integration. To see why, we can use the substitution u = x², du/dx = 2x, to rewrite the integral as (1/2) ∫ [tex]e^u[/tex] du. This integrates to (1/2) [tex]e^u[/tex] + C, which we can substitute back as (1/2) [tex]e^{x^2[/tex] + C to get the most general form of the antiderivative.
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Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Relations and Functions”Below is an example of one.
——————————————————————
Example :
For the problem below read the scenario and answer the questions.
Tai volunteered to sell tickets to an upcoming school play. There are a total of 75 tickets available for a cost of $3 each.
Let M represent the total amount of money she receives from ticket sales and t represent the number of tickets.
A) Write a function M(t) to represent the total amount of money Tao receives from ticket sales.
B) What is the domain of the function? Explain your reasoning.
——————————————————————
2. Answer each question and write a brief step by step process on how you got the answer to each of your questions.
The examples and solutions to the functions are illustrated below based on the information given.
How to illustrate the functions?1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.
The function will be:
C = 100 + (95 × p)
C = 100 + 95p
2nd example: The cost of a pen is $5. Find the cost of s pens.
The function will be:
C = 5 × p
C = 5p
3rd example: Calculate the total amount for m tickets if each ticket is $20.
The function will be;
C = 20 × m
C = 20m
4th example: Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.
C = (2 × g) + (3.40 × d)
C = 2g + 3.4d
5th example: The average age of k number of boys is 7. Find their total age.
The function will be:
a = (7 × k)
a = 7k
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Question 1: Akira sells lemonade at 50 cents a glass. Let m be the amount of money they make in total for g glasses. Akira only has enough lemonade for 20 glasses.
A) Write a function m(g) to represent the total money (in dollars) they make from lemonade sales.
B) What is the domain of the function? Why?
Answer:
A) m(g) = 0.5g
This is since she makes 0.5 dollars per glass
B) The domain is [tex]0 \leq g \leq 20[/tex] where g is an integer. This is since it's impossible to make less than 0 glasses and they cannot make more than 20.
Question 2: Danyon sells CD's at $20 per CD. He has only 15 CD's left.
A) Write a function m(c) to represent the total money he makes from selling c CD's.
B) What is the domain of the function? Why?
Answer:
A) m(c) = 20c, as he makes 20 dollars per CD.
B) The domain is [tex]0 \leq c \leq 15[/tex] where c is an integer, as he can't make less than 0 CD's, and he has only 15 left.
Question 3: A factory is capable of making 60 units per hour. The factory can only run for 24 hours before cool down, and 150 units have already been made.
A) Write a function u(h) to represent the number of units after h hours.
B) What is the domain of the function? Why?
Answer:
A) u(h) = 60h + 150 as it makes 60 units per hour and 150 are already made.
B) The domain is [tex]0 \leq h \leq 24[/tex] as the factory can't run for negative hours and has to cool down after 24 hours.
Question 4: Alazne sells sunglasses at $7 per pair. She has only 30 left before she needs to re-stock.
A) Write a function m(s) which calculates the amount of money she makes after selling s sunglasses.
B) What is the domain of the function? Why?
Answer:
A) m(s) = 7s, as she gets $7 per pair of sunglasses
B) [tex]0 \leq s \leq 30[/tex] where s is an integer, one cannot have a fraction of a pair and she only has 30. She also cannot sell negative sunglasses.
Question 5: Lincoln works at a burger joint in the summer. He makes $3 from every burger he makes. He already has $22 saved. He cannot make more than 10 burgers a day.
A) Write a function m(b) which calculates how much money he gets after making b burgers.
B) What is an appropriate domain for this function?
Answer:
A) m(b) = 3b + 22, as he already has 22 dollars and makes 3 more for every burger.
B) [tex]0\leq b\leq10[/tex], where b is an integer. This is since he cannot make a fraction of a burger, negative burgers, or more than 10 burgers.
A rectangle has a length of (3x - 1) and a width of (x + 1). part a determine the perimeter and area of the rectangle as polynomials. part b determine the perimeter and area of the rectangle if x equals 5. part c determine the perimeter and area of the rectangle if x equals 8.
Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
Lets try to solve out the problem,
Length = 3x-1
Width = x+1
Perimeter = 2(l+b)
Area = l*b
Perimeter= 2 (3x-1 + x+1)
P= 8x
Area = (3x-1) (x+1)
=> 3x(x+1) -1 (x+1)
=> 3x^2 + 3x -x -1
=> 3x^2 + 2x -1.
Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
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If you live in Miami, then you live in
Florida.
Choose the equivalent statement.
A. If you live in Florida, then you live in Miami.
B. If you don't live in Miami, then you don't live in
Florida.
C. If you don't live in Florida, then you don't live in
Miami.
Answer: the answer is c.
Step-by-step explanation:
The length of a rectangle is 4 times the width. If the perimeter is to be less than or equal to 100 meters. What are the possible values for the width
The possible values for the width is w≥10.
Given that the length of a rectangle is 4 times the width and perimeter is to be less than or equal to 100 meters.
The perimeter of a rectangle is the total distance of its four outer boundaries. The perimeter of the object is twice the length and width of the object. This calculation is made using the formula:
perimeter = 2(length + width).
Here Perimeter=100 and length=4w
Substituting these values in the formula to find width, and we get
100≤2(4w+w)
100≤2(5w)
Divide both sides by 2, and we get
100/2≤(2(5w))/2
50≤5w
Divide both sides by 5, and we get
50/5≤5w/5
10≤w
Hence, the possible value for width when the length of a rectangle is 4 times the width is w≥10.
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Which equation represents exponential decay? * a y=3^x-4 b y=2(4)^x c y=1/2(3)^x d: y=6(1/3)^x
The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]
Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].
Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].
Decay means when x value increases ,the y value decreases.
We haveto put 3 values for x in the equations to check.
1)y=[tex]3^{x} -4[/tex]
put x=0,y=-3
put x=1, y=-1
put x=2, y=5
No,itdoes not represents exponential decay.
2) y=2[tex]4^{x}[/tex]
put x=0,y=2
put x=1, y=8
put x=2, y=32
No,it does not represents exponential decay.
3) y=[tex]3^{x}/2[/tex]
put x=0,y=0.5
put x=1, y=1.5
put x=2, y=4.5
No,it does not represents exponential decay.
4)y=6[tex](1/3)^{x}[/tex]
put x=0,y=6
put x=1, y=2
put x=2, y=0.67
Yes ,it represents exponential decay.
Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].
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Total area=
Help me please
Thanks so much
The side lengths of ABC are 2, 5, and 6, and DEF has side lengths of 12, 30, and 36. Find the ratios of the lengths of the corresponding sides of ABC
to DEF. Are the two triangles similar? Explain. Determine which two of the three given triangles are similar. Find the
scale factor for the pair.
Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.
What are Similar Triangles?The ratios of the corresponding sides of similar triangles are equal, because they are proportional.
If triangles ABC and DEF are similar triangles, then:
AB/DE = BC/EF = AC/DF
Plug in the given values
2/12 = 5/30 = 6/36 = 1/6
This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.
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help please i’m not sure if it’s c
the answer is infact c!
If f(x)= 2x/7+4 which of the following is the inverse of f(x)
The inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.
What is the inverse of the function?
Given the function; f(x)= 2x/7 + 4
First. we write the function as an equation then interchange the variables.
y = 2x/7 + 4
x = 2y/7 + 4
We solve for y.
2y/7 = x - 4
2y = 7x - 28
y = 7x/2 - 28/2
y = 7x/2 - 14
Therefore, the inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.
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Adam runs 100m in 14.5 seconds. Jenny runs the same distance 10% faster. How long does it take for Jenny to finish?
The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds
PercentageDistance Adam runs = 100mTime taken by Adam = 14.5 secondsDistance Jenny runs = 100mTime taken by Jenny = 14.5 - (10% × 14.5)
= 14.5 - (0.1 × 14.5)
= 14.5 - (1.45)
= 13.05 seconds
Therefore, the time taken for Jenny to run the same distance is 13.05 seconds
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Need help checking my answer for #1 (solving special inequalities)
Inequality are expressions not separated by an equal sign. The inequality shown has no solution
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality expression
2(x-3) ≤ 3 + 2x
Expand
2x - 6 ≤ 3 + 2x
2x - 2x ≤ 3 +6
0x ≤ 9
x≤9/0
Hence the inequality shown has no solution
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please help me 20 points
Out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style. This can be obtained by using formula of probability and multiplying the total number of pizzas.
Find the expected value:The formula for Expected value:
EV = P(X) × n
where EV is the expected value and P(X) is the probability of X and n is the total number.
In the question it is given that,
Thin crust ⇒ number of thin crust sold = 307 Thick crust ⇒ number of thick crust sold = 224Stuffed crust ⇒ number of stuffed crust sold = 161Pan style ⇒ number of pan style sold = 191First we have to find the probability of stuffed crust or pan style,
P( stuffed crust or pan style) = P(stuffed crust) + P(pan style)
The number of stuffed crust and pan style = 161 + 191 = 352
The total number of crusts sold are ⇒ 307 + 224 + 161 + 191 = 883
⇒ P( stuffed crust or pan style) = 161/883 + 191/883
= 352/883
The expected value of stuffed crust or pan style,
n = 2000, P(X) = 352/883
EV = P(X) × n = (352/883) × 2000 = 797.28 ≈ 797
Hence out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style.
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MULTIPLE CHOICE
Question 13
Which best describes the range of f(x)?
Based on the function, the range of f(x) = 2(3)^x can best be described as y > 0.
What is the range of f(x) = 2(3)^x?When a number is raised to a power, the result will always be positive even if the number is raised to a negative number.
This means that 3^x will always be positive which means that 2(3)^x will also be positive. y will therefore always be greater than 0.
Full question is:
Which best describes the range of the function f(x) = 2(3)^x?
y > 0
y ≥ 0
y > 2
y ≥ 2
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how many cards from a standard deck must be drawn to guarantee atleast 3 cards of the same suit have been drawn, pidgeon hole
The number of cards which must be drawn from the standard deck is 12.
Given a standard deck of cards.
We have to find the number of cards to be drawn so that we will get atleast 3 cards from each suit. Because they have used atleast in the question so the cards can be more also so we have to reach at minimum level of cards to be drawn to guarantee atleast 3 cards of the same suit.
Number of suits in a standard deck= 4 (Clubs, Hearts, Diamond, Spades)
Cards in 1 suit=13
We need atleast 3 cards of the same suit so we need atleast 3*4=12 cards. (3 from each suit)
Hence the minimum cards which must be drawn to get atleast 3 cards of the same suit is 12.
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i need major help completing math questions (im terrible at it.)
Answer:
78.5 inches square is the answer
Step-by-step explanation:
area-3.14*(5)^2
In our solar system, 6 of the 8 planets have moons.
What percentage of the planets have moons?
Answer:
75%
Step-by-step explanation:
On four consecutive statistics quizzes, you receive the scores: 86 96 100 98 what is your median quiz score?
Answer:
98
Step-by-step explanation:
96+100=196
196÷2=98
Answer:
97.
Step-by-step explanation:
86 96 100 98
Place them in order:
86 96 98 100
The median is the middle value of an ascending sequence of numbers.
As there is an even number of values the median is the mean of the 2 middle ones:
So here it is (96 + 98) / 2
= 97.
The standard deviation tells us a. the average value of the scores. b. the relative standing of a particular score. c. the skewness of the distribution. d. the dispersion of the scores.
Answer:
D.
Step-by-step explanation:
Standard deviation tells us the dispersion of data/scores around the mean.
We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
What is the standard deviation?A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.
We use the following formula to compute the standard deviation:
[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]
In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.
How to solve the question?In the question, we are asked to tell what standard deviations tell us from the given options.
From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
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A train leaves Geneva at 09:10 and arrives at Verona at 14:10 the distance from Geneva to Verona is 390 km calculate the average speed of the train in km/h
Mario is 63 years older than his grandson Jonas. How many years ago was Mario's age 10 times Jonas's age if Mario's age is currently four times Jonas's age?
Answer:
14 years ago
Explanation:
Let Mario's age be m, Jonas age be j.
From, Mario is 63 years older than Jonas
Equation 1: m = j + 63
From, Mario's age is four times Jonas age
Equation 2: m = 4j
Solve them by substitution:
m = j + 63
4j = j + 63
4j - j = 63
3j = 63
j = 21
Find Mario's age:
m = j + 63
m = 21 + 63
m = 84
Follow this steps:
m - y = 10(j - y)
84 - y = 10(21 - y)
84 - y = 210 - 10y
-y + 10y = 210 - 84
9y = 126
y = 14
The answer is 14 years ago.
Let Mario's age be M, and Jonas' age be J.
The formed equations :
M = J + 63M = 4JTo find their current ages, substitute the 2nd equation in the 1st equation.
4J = J + 63
3J = 63
J = 21
M = 4(21)
M = 84
For Mario to be 10 times Jonas' age, he has to be an age that is a multiple of 10.
Case (1) : Mario's age = 80
Subtract 4 from both their ages.
Mario : 84 - 4 = 80
Jonas : 21 - 4 = 17
17 × 10 ≠ 80
Case (2) : Mario's age = 70
Subtract 14 from both their ages.
Mario : 84 - 14 = 70
Jonas : 21 - 14 = 7
7 × 10 = 70
Write the equation for a parabola with a focus at (7,2) and a directrix at y = -2 y = ?
Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]
How to find the equation of parabola with focus and directrix ?
We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]
So [tex]k+p=2[/tex]......(a)
And directrix of the parabola
[tex]y=k-p\\=-2[/tex]
[tex]k-p=-2[/tex]........(b)
So add the equation (a) AND (b)
[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]
Equation of the parabola with directrix and focus
[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]
Substitute all the values
[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
Answer:
[tex]\sqrt{\frac{15}{2} }[/tex] or 2.738
Step-by-step explanation:
Let’s just look at the triangle on the top with the [tex]\sqrt{10}[/tex] on the top and x on the bottom. (Basically the top half to the equilateral triangle)
There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=[tex]\frac{1}{2}(\sqrt{10})[/tex] or [tex]\frac{\sqrt{10} }{2}[/tex]
Plugging these values into the equation:
x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}
[tex]x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}[/tex]
[tex]x^{2} =10-\frac{10}{4}[/tex]
[tex]x^{2} =\frac{15}{2}[/tex]
[tex]x=\sqrt{\frac{15}{2} }[/tex]
This approximately equals 2.738
Answer:
[tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex](it's the same thing)
Step-by-step explanation:
Because the triangle is equilateral, all other sides of the triangle are also [tex]\sqrt{10}[/tex]. Also, x is the altitude of this triangle as it forms a right angle with the base and is therefore perpendicular. We know that this triangle is equilateral and in any triangle that has at least two sides that are equal(in other words isosceles), the altitude is also the median and angle bisector. A median would cut the side it reaches into half. So, x would cut the base into two equal parts. Since the base is [tex]\sqrt{10}[/tex], divide it by two and both halves are [tex]\frac{\sqrt{10}}{2}[/tex]. What we are left with is two right triangles, both with legs [tex]\frac{\sqrt{10} }{2}[/tex] and x. Using the Pythagorean Theorem, we know that [tex]a^{2}+b^{2}=c^{2}[/tex], with [tex]a[/tex] and [tex]b[/tex] being the legs and [tex]c[/tex] being the hypotenuse. So, we plug in the values and get [tex]\frac{\sqrt{10} }{2} ^{2}[/tex][tex]+x^{2}=\sqrt{10}^{2}[/tex]. Squaring, we get [tex]\frac{10}{4}+x^{2}=10[/tex]. This becomes [tex]x^{2}=10-\frac{10}{4}[/tex] which equals [tex]x^{2}=\frac{40}{4}-\frac{10}{4}[/tex]. Finally, [tex]x^{2}=\frac{30}{4}[/tex]. This is [tex]x^{2}=\frac{15}{2}[/tex]. Square rooting this we get [tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex]
What term describes the brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats
Refractory period brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats.
At what time is the volume of blood in the ventricle at a maximum?End-diastolic pressure is at its resting level (end-diastolic pressure) and ventricular volumes are at their maximum value when the heart muscle is relaxed (end-diastolic volume).
What is the state of the heart during systole?
Describe what occurs during systole in the heart. Describe where the blood is sent from each ventricle. Right ventricle transfers blood into the pulmonary artery during ventricular contraction and pumps it to the heart.What are the 4 phases of cardiac cycle?
There are four main stages of activity in the cardiac cycle: Isovolumic contraction, inflow, ejection, and relaxation are the order of events. (See Wiggers graphic, which labels the stages in the following order: 3, 4, 1, and 2, from left to right.)Learn more about Refractory period
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An aircraft seam requires 21 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 23% of all seams need reworking, what is the probability that a rivet is defective
For Part A the probability is 0.0095 and for Part B the probability is
0.0043.
What does defective mean in probability?Probability of defect is perhaps the most important indicator of a manufacturing process's quality. It's a statistical technique used to indicate how often a product will fail during its lifespan, which in turn allows you to estimate the likelihood that an item will result in customer dissatisfaction.
Part A:
The number of rivets=22 rivets
Probability that no rivet is defective= [tex](1-p)^{22}[/tex]
The probability that at least one rivet is defective=1-[tex](1-p)^{22}[/tex]
For 19% of all seams need reworking, probability that a rivet is defective is given by
1-[tex](1-p)^{22}[/tex] = 0.19
[tex](1-p)^{22} = 1-0.19\\(1-p)^{22} = 0.81\\ p=1-\sqrt[22]{0.81} \\p=0.0095[/tex]
Part B:
For 9% of all seams need reworking, probability of a defective rivet is:
1-[tex](1-p)^{22}[/tex] = 0.09
[tex](1-p)^{22} = 1-0.09\\(1-p)^{22} = 0.91\\ p=1-\sqrt[22]{0.91} \\p=0.0043[/tex]
Hence, For Part A the probability is 0.0095 and for Part B the probability is 0.0043.
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What value(s) of x will make x²=81 true?
Answer: 9,-9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
9x9=81
A committee of three people needs to be chosen. There are three men and five women available to serve on the committee. If the committee members are randomly chosen, what is the probability that two of the three people chosen on the committee are women
Answer:
probability of choosing two women over people in a community=⅔
Find the area of the polygon.
Answer:
36
Step-by-step explanation:
Hello!
Area of a Parallelogram: [tex]A = b*h[/tex]
b = baseh = heightGiven our shape:
Base = 9height = 4Don't forget, the height is the altitude to the base, which means it forms a perpendicular intersection. The height is not the slant height of the parallelogram.
Find the Area[tex]A = b*h[/tex][tex]A = 9*4[/tex][tex]A = 36[/tex]The area is 36 un².
__________ 11A. In Circle O, it is given that m∠A = 20°.
Find m∠B.
Answer:
70 degrees.
Step-by-step explanation:
As AB is a diameter M < C = 90 degrees.
Therefore m < B = 90 - 20 = 70.
Find the additive inverse of the following. (a) -4 (b) -18 (c) 620 (d) 60 (e) -244 (f) -8921
The additive inverse is:
(a) 4 (b) 18 (c) -620 (d) -60 (e) 244 (f) 8921
What is additive inverse?
The additive inverse of a number x is the number that, when added to x yields zero.
It is shown as [tex]x+(-x)=0[/tex]
To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.
The additive inverse of the given numbers are:
(a) 4
(b) 18
(c) -620
(d)-60
(e) 244
(f) 8921
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Which series is convergent? check all that apply. sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction sigma-summation underscript n = 1 overscript infinity endscripts startfraction n squared minus 1 over n minus 2 endfraction sigma-summation underscript n = 1 overscript infinity endscripts (one-fifth) superscript n sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction) superscript n sigma-summation underscript n = 1 overscript infinity endscripts startfraction 1 over 10 endfraction (3) superscript n
These series show convergence of series which are
sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction
sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)
According to the statement
we have given the some series and we have to find that the out of these series which series is convergent.
So, For this purpose we have to check the convergence of series.
So,
we know that the for the convergent of series there is a one condition and if those condition will satisfy on the series then the series is convergent and if not then series is divergent.
So, the condition for convergent is a series converges if the absolute value of the sum of any finite number of sequential terms can become arbitrary small by starting the addition from a term which is far enough. So, if this condition is not satisfied the series diverges.
When we apply this condition on all given series then only 2 series satisfy this condition which is
sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfractionsigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)So, These series show convergence of series which are
sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction
sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)
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Answer:
B. The series converges because it has a sum of 2/3
Here are the answers for the rest of the assignment:
C.
B.
C and D
A and C
B and D
C.
B. 0.31 and A. 0.0025
B. 1.0317 and C. 1.9683
(please read below)
Step-by-step explanation:
Had the assignment and these are the correct answers, enjoy :)
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