Please Help!
For Ln=1n∑ni=1i−1n , given Ln as indicated, express their limits as n→[infinity] as definite integrals, identifying the correct intervals
Answers
The limit of Ln as n approaches infinity is -1/2, and it can be expressed as the definite integral ∫0¹ (x - 1) dx over the interval [0, 1].
To express the limit of Ln as n approaches infinity as a definite integral, we can use the definition of the definite integral as the limit of a Riemann sum. We can divide the interval [0, 1] into n subintervals of equal width Δx = 1/n, and evaluate Ln as the limit of the Riemann sum:
Ln = 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]
where f(x) = x - 1 is the function being integrated.
Taking the limit as n approaches infinity, we have:
lim(n→∞) Ln = lim(n→∞) 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]
= ∫0¹ (x - 1) dx
where we have used the fact that the limit of the Riemann sum is equal to the definite integral of the function being integrated.
Therefore, the limit of Ln as n approaches infinity is equal to the definite integral of (x - 1) over the interval [0, 1].
So,
lim(n→∞) Ln = ∫0¹ (x - 1) dx = [x¹ - x] from 0 to 1
= [1/2 - 1] - [0 - 0]
= -1/2
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Related Questions
I am having a bit of trouble with this
write an expression, with fewer terms, that is equivalent to 9x+6-4x+9
Answers
Answer:
5x + 15
Step-by-step explanation:
Given
9x + 6 - 4x + 9 ← collect like terms
= (9x - 4x) + (6 + 9)
= 5x + 15
PLEASE help plssss no links and silly answers
Answers
Answer:
(H)
Step-by-step explanation:
Less than signs are <
Greater than signs are >
Since in this case x is the number
7 has to be less than x which is x<7
Answer:
f
Step-by-step explanation:
What is the solution to the equation: 2x-5 = -x+7
A: x=4
B: x=12
C: x=2
D: x=-4
Answers
Answer:
D: x=-4
Step-by-step explanation:
1. Identify each of the following statements as true of false and explain your reasoning in full sentences. The domain of discourse is the integers.
(a) ∃x∀y(y > x)
(b) ∀y∃x(y > x)
(c) ∃x(x = 0 → x = 1)
2. Write the formal negation of the following statements. Your negation must not contain any explicit negation symbols.
(a) ∀x∃y(2 < x ≤ y)
(b) ∀y∃x(y > 0 → x ≤ 0)
3. Negate verbally:
(a) "All people weigh at least 100 pounds."
(b) "Somebody did not see any animals in the zoo"
4. If P and Q are predicates over some domain, and if it is true that∀x(P(x)∨ Q(x)), must ∀xP(x)∨∀xQ(x) also be true? Explain.
Answers
The domain of discourse is the integers is smaller integer
What is Integer?
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
1.(a) ∃x∀y(y > x)
The statement is False
it is impossible to find a single integer x that has the property that all integer y are bigger that it. for any integer x, the integer y =x-1 is smaller
(b) ∀y∃x(y > x)
the statement is true for every integer y, we can find a integer x that is smaller, for example x=y-1
(c) ∃x(x = 0 → x = 1)
The statement is True
there exist x such that (x = 0, x=1). in this statement when we select x =1. this statement is true regardless of x not equal to 0 therefore this statement is true if x=1 when x=1
2. (a) ∀x∃y(2 < x ≤ y)
we know
∀xP(x)=∃y(P(x))
∃xP(x)=∃y(P(x))
now apply de morgan law
∃x∀(y)=2>x v x>y
(b) ∀y∃x(y > 0 → x ≤ 0)
we know that A-B = A V B
∀y∃x (Y<0 V X< 0)
∀y∃x (Y<0 : X< 0)
3.(a) Given : All people weigh at least 100 pounds.
The negation is : Some people weigh less than 100 pounds. ( All negates to some, at least negates to less than )
(b) The statement is : Somebody did not see any animals in the zoo.
Equivalently : Somebody see no animals in the zoo.
Negation : Everybody saw some animals in the zoo. ( Somebody negates to everybody, No animals negates to some animals )
4. P(x,y): x is friends with y.
Then the given translates to " For all x there is a person y and a person z such that if y and z are not the same people that x and y are friends and x and z are friends."
The given statement is False. For every person x, we can always find two distinct persons y and z such that x is friends with y and y is friends with z. But, we reach a contradiction when we consider the case when x has only one friend. Then for that particular person x, we can find a person y such that P(x,y) but we cannot find a person z such that P(x,z). Hence, in that case, the statement is FALSE.
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Which ratio is equal to 15:20?
a: 5:10
b: 18:25
c:21:28
d: 24:30
Answers
Answer:
C - 21:28
Step-by-step explanation:
this is solved by a little bit of trial and error. divide the possible answer numerators by 15, and check if it's the same for the denominator.
For C I did this:
Divided the denominators: 28 ÷ 20 = 1.4....so that's 1.4.
Let's test it out for the numerator now. 21 ÷ 15 = 1.4.
So there's your answer.
What is the quotient and remainder for 19÷420
Answers
=
22 Remainder 2
which of the following points is on the unit circle
Answers
The required answer is the all of the given points (A, B, C, and D) are on the unit circle.
The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. Points on the unit circle can be represented by their coordinates (x, y), where x is the cosine of the angle and y is the sine of the angle.
To determine which of the following points is on the unit circle, we need to check if the coordinates satisfy the equation x^2 + y^2 = 1. If the coordinates satisfy this equation, then the point is on the unit circle.
consider the points given and check if they are on the unit circle:
- Point A: (1, 0)
- Point B: (0, -1)
- Point C: (-√2/2, √2/2)
- Point D: (0, 1)
Checking each point:
- Point A: (1, 0)
- 1^2 + 0^2 = 1 + 0 = 1
- The coordinates satisfy the equation, so point A is on the unit circle.
- Point B: (0, -1)
- 0^2 + (-1)^2 = 0 + 1 = 1
- The coordinates satisfy the equation, so point B is on the unit circle.
- Point C: (-√2/2, √2/2)
- (-√2/2)^2 + (√2/2)^2 = 2/4 + 2/4 = 4/4 = 1
- The coordinates satisfy the equation, so point C is on the unit circle.
- Point D: (0, 1)
- 0^2 + 1^2 = 0 + 1 = 1
- The coordinates satisfy the equation, so point D is on the unit circle.
In conclusion, all of the given points (A, B, C, and D) are on the unit circle because their coordinates satisfy the equation x^2 + y^2 = 1.
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Question 2 A roll of material is 2 meters long. How many pieces of material can be cut from the roll if each piece is to be (2)/(5) meters long?
Answers
If a roll of material is 2 meters long, then the number of pieces of material that can be cut from the roll if each piece is to be 2/5 meters long is 5.
To find how many pieces of material can be cut from the roll, follow these steps:
To find the number of pieces of material that can be cut from the roll if each piece is to be 2/5 meters long, we need to divide the length of the roll by the length of each piece.Substituting the values, we get the number of pieces = 2 / (2/5) ⇒Number of pieces = 2 * (5/2) ⇒Number of pieces = 5 piecesTherefore, 5 pieces of material can be cut from the roll if each piece is to be 2/5 meters long.
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for how many integers $n$ between 1 and 1990 is the improper fraction \[\frac{n^2 7}{n 4}\] not in lowest terms?
Answers
Between 1 and 1990, there are 2,475 integers for which the improper fraction (n^2 * 7) / (n * 4) is not in its lowest terms.
To determine when the fraction is not in lowest terms, we need to find values of n for which the numerator and denominator share a common factor greater than 1. Simplifying the fraction, we get (n * 7) / 4. For the fraction to be in lowest terms, n and 4 must be coprime, meaning they have no common factors other than 1. To find the values of n that violate this condition, we need to identify the multiples of 4 within the range 1 to 1990. There are 497 multiples of 4 in this range. However, since we are looking for values of n, we need to subtract 1 to exclude the multiple 0, yielding 496. Therefore, there are 496 values of n that do not satisfy the coprime condition. Subtracting this from the total number of integers in the range (1990 - 1 = 1989), we find that 1989 - 496 = 1493 integers yield the fraction in lowest terms. Finally, subtracting this number from the total number of integers (1990 - 1), we find that 1990 - 1493 = 497 integers give the fraction (n^2 * 7) / (n * 4) in lowest terms.
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Really need help asap thank you!!!
Answers
Answer: 20°
Step-by-step explanation:
Let's call angle 1 x and angle 2 y
We know that x is three times greater than y, and that means that we can write it like this:
3y = x pls let me know if this part is confusing
Then we can write this entire equation:
3y + y = 80 remember, x = 3y
4y = 80
y = 20
adding 3 to some number , then multiplying the result by 7 give 28 what was the original number?
pls answer me now
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The required number is :
\(1\)\( \large \boxed{ \mathfrak{Explanation}}\)
Let the number be represented as " x "
from the given statement we can infer that :
\(7(x + 3) = 28\)So, let's find the value of " x " from the given equation ~
\(x + 3 = 28 \div 7\)\(x + 3 = 4\)\(x = 4 - 3\)\(x = 1\)Answer:
Let the required original number be " x "
According to the given problem,
\(7(x + 3) = 28 \\ (x + 3) = \frac{28}{7} \\ (x + 3) = 4 \\ x =(4 - 3) \\ \boxed{x = 1}\)
Hence, the original number is 1.1 is the right answer.
IF I SPEND $6,300 OUT OF $21,000 WHAT PERCENT DID I SPEND
Answers
Answer: 30%
Step-by-step explanation: Solution for 6300 is what percent of 21000: 6300:21000*100 = (6300*100):21000 = 630000:21000 = 30. Now we have: 6300 is what percent of 21000 = 30.
if we take 21000(origin amount) to be the 100%, what's 6300 off of it in percentage?
\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 21000 & 100\\ 6300& x \end{array} \implies \cfrac{21000}{6300}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{10}{3} ~~=~~ \cfrac{100}{x}\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30\)
solve the following using BEDMAS
5X4 -(3+1)2÷2
Answers
the value of the expression is 12.
To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.
The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.
It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.
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Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
Answers
Answer:
1694
Step-by-step explanation:
State the explicit formula for the sequence below and find the 8th term.
-4, 16, -64, 256,...
O an = -4(4)n-1; n = 8 is-262,144
O an = -4(-4)-1; n = 8 is 65,536
O an = 4(4)n-1; n = 8 is 65,536
O a = 4(-4)n-1; n = 8 is 261,144
6.25 pts
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Answers
The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536
The given sequence is -4, 16, -64, 256,...
If we observe the sequence it is a geometric sequence
aₙ=a.rⁿ⁻¹
a is the first term and r is the common ratio
From the sequence the first term is -4 and common ratio is -4
aₙ=(-4).(-4)ⁿ⁻¹
Plug in the value n as 8
a₈=(-4).(-4)⁷
The value of minus four power seven is minus sixteen thousand three hundred eighty four
a₈=(-4)(-16384)
When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six
a₈= 65536
Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536
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Help! I keep seeing different answers! Thank you!!
Answers
Mackenzie is a waitress at a restaurant. Each day she works, Mackenzie will make a guaranteed wage of $25, however the additional amount that Mackenzie earns from tips depends on the number of tables she waits on that day. From past experience, Mackenzie noticed that she will get about $15 in tips for each table she waits on. How much would Mackenzie expect to earn in a day on which she waits on 13 tables? How much would Mackenzie expect to make in a day when waiting on tt tables?
Answers
Answer:
$25 + $15tt
Step-by-step explanation:
On a day when Mackenzie waits on 13 tables, she will earn a total of $25 in guaranteed wage plus $15 in tips for each table, for a total of $25 + (13 tables * $15/table) = $25 + $195 = $220.
If Mackenzie waits on tt tables, she will earn a total of $25 in guaranteed wage plus $15 in tips for each table, for a total of $25 + (tt tables * $15/table) = $25 + $15tt.
So, if Mackenzie waits on tt tables, she can expect to earn $25 + $15tt.
PLEASE HELP I WILL GIVE EXTRA POINTS AND BRAINALIST to the first person
Answers
Answer:
A.
Step-by-step explanation:
The answer is A.
A homeowner is building a circular fire pit in his backyard. He plans to outline the pit with bricks and cover the space inside the pit with sand. The homeowner has decided to build the pit with a diameter of 3 feet.
In order to know how many bricks to buy, the homeowner must know the distance around the outside of the pit. Calculate both the exact distance and the approximate distance.
In order to know how much sand to buy, the homeowner must know how much space needs to be covered inside the pit. Calculate both the exact area and the approximate area.
Answers
Answer:
To calculate the distance around the outside of the circular fire pit, also known as the circumference:
Exact distance:
Circumference = pi x diameter
C = pi x 3 feet
C = 3.14 x 3 feet
C = 9.42 feet
Approximate distance:
Circumference = 2 x radius x pi
Radius = diameter / 2 = 1.5 feet
C = 2 x 1.5 feet x 3.14
C = 9.42 feet
Therefore, the exact distance around the outside of the circular fire pit is 9.42 feet, and the approximate distance is also 9.42 feet.
To calculate the area inside the circular fire pit:
Exact area:
Area = pi x (radius)^2
Area = 3.14 x (1.5 feet)^2
Area = 7.07 square feet
Approximate area:
Area = (diameter / 2)^2 x pi
Area = (1.5 feet)^2 x 3.14
Area = 7.065 square feet
Therefore, the exact area inside the circular fire pit is 7.07 square feet, and the approximate area is 7.065 square feet.
4) Anna uses 4 gallons of gas to drive 160 miles on the
highway. If she travels at the same rate, how many miles can she drive on 7 gallons of gas
A. 40 miles
B. 80 miles
C. 200 miles
D. 280 miles
Answers
Answer:
D. 280miles
*Step by step explanation*
miles= 160miles × 7gallons / 4 gallons
miles = 280 miles
A store is having a sale where winter clothes are 60% of the original price. A sweater is on sale for $30. What was the original price of the sweater?
Answers
Answer:
50
Step-by-step explanation:
Bruh
please help me i have no idea how
Answers
Answer:
B
Step-by-step explanation:
ANSWER THIS PLEASE !!!!
1) What is six thousand three hundred and fifty millilitres to the nearest litres?
2) A bottle of juice holds three-fourths of a litre. How many millilitres of juice does it hold?
3) A one-litre milk carton is one quarter full. How much milk is left in the carton?
Answers
Answer:
1. 6.35
2. 750
Step-by-step explanation:
Consider the function f(x)=1/3(6)x. What is the value of the growth factor of the function?
Answers
Answer:
F = 2
Step-by-step explanation:
Answer:6
Step-by-step explanation:i did the quiz
please help!!! find value of x
Answers
Answer:
15
Step-by-step explanation:
10x2.5 equals 25
6x2.5 equals 15
Hello I need help understanding this question please explain well!
An Etsy seller charges 0.65 per pound for shipping. Write an equation for the cost(y) of shipping x pounds. Use it to determine the cost of shipping a 10-pound package.
Answers
Answer:
Uhh
Step-by-step explanation:
divide x³ + 5x² + 7x – 2 by x + 3.
Answers
Answer:
= x^3 + 5x^2 + 5x + 3
Step-by-step explanation:
Let's simplify: Step-by-Step.
x^3 + 5x^2 + 7x − 2x + 3
=x^3 + 5x^2 + 7x + − 2x + 3
Combine Like Terms:
=x^3 + 5x^2 + 7x + − 2x + 3
=(x^3) + (5x^2) + (7x + − 2x) + (3)
=x^3 + 5x^2 + 5x + 3
Answer:
=x^3 + 5x^2 + 5x + 3
HOPE THIS HELPS!
PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN
Answer:
(x³ + 5x² + 7x – 2) /(x+3)=(x^2+2x+1)-5/(x+3)
Please help me I really can’t figure this out
Answers
Answer:
can you upload a bigger picture
V = 1/3 (3.14) ( 3^2) (5)
V = 47.1 cubic inches
For the candy: V = 4/3 x pi x r^3
V = 4/3 (3.14) (1.5^3)
V = 14.13 cm
Hayden rides his bicycle to and from school every day. in 5 days, he wrote a total distance of 9 kilometers. at this rate how many kilometers will he ride in 60 days 
A. 108 km B. 105 km C. 45 km D. 33 km
Answers
Answer:
A. 108
Step-by-step explanation:
60 x 9 = 540
540 divided by 5 = 108
Answer:
A
Step-by-step explanation:
5 days he rode 9 kilometers
60 divided 5=12
12x9=108
In the figure, PA is tangent to the dime, PC is tangent to the quarter, and PB is a common
internal tangent. How do you know that PA PB PC?
O The segments are congruent by the Tangent Line to Circle Theorem.
o Because all of the radii are congruent, the tangent line segments are congruent too.
Because PÅ is the angle bisector of ZAPC, APAB and APBC are congruent isosceles triangles.
O The segments are congruent by the External Tangent Congruency Theorem.
Answers
The three tangent segments to the two circles that are in contact, are congruent, according to tangent theorem. The correct option is therefore;
The segments are congruent by the tangent line to a circle theoremHow can the relationship between the segments be found?According to the two tangents theorem, two tangents segments to the same circle that meet at a common external point are congruent segments.
Therefore;
The tangents to the dime, PA and PB are congruent.
Similarly, PB is congruent to PC
By the property of equality, we have;
PA = PB = PC
The correct option is therefore;
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