Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 1- cos 8x lim x→0 How should the given limit be evaluated? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A.Use I'Hopital's Rule exactly once to rewrite the limit as lim OB. Multiply the expression by a unit fraction to obtain lim ( x→0 C. Use l'Hôpital's Rule more than once to rewrite the limit in its final form as lim x-+0 O D. Use direct substitution.
Answers
To evaluate the limit lim x→0 (1 - cos 8x), the appropriate method is to use l'Hôpital's Rule once. The correct choice is A: Use l'Hôpital's Rule exactly once to rewrite the limit as lim x→0 (8sin 8x)
The given limit is of the form (1 - cos 8x) as x approaches 0. To evaluate this limit, we can use l'Hôpital's Rule, which states that if the limit of the ratio of two functions as x approaches a is an indeterminate form (such as 0/0 or ∞/∞), then taking the derivative of both the numerator and denominator can help simplify the expression.
In this case, differentiating the numerator and denominator yields:
lim x→0 (1 - cos 8x) = lim x→0 (0 - (-8sin 8x)) = lim x→0 (8sin 8x)
Now, we can directly evaluate the limit by substituting x = 0 into the expression:
lim x→0 (8sin 8x) = 8sin(0) = 8(0) = 0
Therefore, the correct choice is A: Use l'Hôpital's Rule exactly once to rewrite the limit as lim x→0 (8sin 8x).
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Related Questions
Factor.
9x2−49y2
Enter your answer in the box.
Answers
Answer:
(3x + 7y)(3x - 7y)
Step-by-step explanation:
This is the difference of two squares.
9x² - 49y² = (3x + 7y)(3x - 7y)
Quadrilateral LMNO is reflected about the x-axis.
What are the coordinates of the images of vertices L, M, N, and O?
A. L’(2, 5), M’(2, -1), N’(5, -2) and O’(6,-4)
B. L’(-5, 2), M’(-2, -1), N’(-5, -2) and O’(6,-4)
C. L’(2, -5), M’(2, -1), N’(5, -2) and O’(6,-4)
D. L’(2, -5), M’(2, -1), N’(-5, -2) and O’(-6,-4)
(first correct answer gets branleist)
Answers
C.)
L’(2, -5), M’(2, -1), N’(5, -2) and O’(6,-4)
Answer:
c i did the quiz
Step-by-step explanation:
meredith is a general surgeon who performs surgeries such as appendectomies and laparoscopic cholecystectomies. the average number of sutures that meredith uses to close a patient is 37, and the standard deviation is 8. the distribution of number of sutures is right skewed. random samples of 32 are drawn from meredith's patient population, and the number of sutures used to close each patient is noted. use the central limit theorem to find the mean and standard error of the sampling distribution. select the statement that describes the shape of the sampling distribution. group of answer choices unknown the sampling distribution is normally distributed with a mean of 37 and standard deviation 1.41. the sampling distribution is right skewed with a mean of 37 and standard deviation 8. the sampling distribution is normally distributed with a mean of 37 and standard deviation 8. the sampling distribution is right skewed with a mean of 37 and standard deviation 1.41.
Answers
The statement that accurately describes the form of the sampling distribution is:The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.
According to the central limit theorem, regardless of how the population distribution is shaped, the sampling distribution of the sample mean will be approximately normally distributed for a sufficiently large sample size.
For this situation, irregular examples of 32 are drawn from Meredith's patient populace, which fulfills the state of a sufficiently huge example size. The central limit theorem can be used to determine the sampling distribution's mean and standard error.
In this instance, the population mean, which is 37, is equal to the mean of the sampling distribution.
The population standard deviation divided by the square root of the sample size is the sampling distribution's standard error. For this situation, the standard mistake is 8 partitioned by the square foundation of 32, which is around 1.41.
Therefore, the statement that accurately describes the form of the sampling distribution is:
The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.
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solve the proportion b+4/5=7/4
Answers
Step-by-step explanation:
When adding or subtracting fractions, they must have a common denominator....20 is the easiest for these...this then becomes
b + 16/20 = 35/20 now subtract 16/20 from both sides of the equation
b = 35/20 - 16/20
b = (35-16)/20 = 19/20
Which best describes the circumcenter of a triangle?
A. The point where the three medians of the triangle intersect
B.The point where the three angle bisectors of the triangle intersect
C.The point where the perpendicular bisectors of the three sides of the triangle intersect
D.The point where the three altitudes of the triangle intersect
Answers
Answer:
C. The point where the perpendicular bisectors of the three sides of the triangle intersect.
Step-by-step explanation:
A number of centers of a triangle are defined. The circumcenter is the center of the circumscribing circle. The incenter is the center of an inscribed circle. The centroid is the center of balance of a triangle of uniform mass density.
Center definitionsThe centers defined by descriptions A through D are ...
A. centroid -- coincident point of medians
B. incenter -- coincident point of angle bisectors
C. circumcenter -- coincident point of side perpendicular bisectors
D. orthocenter -- coincident point of altitudes
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Select two options.
Answers
The statements that are true regarding triangle XYZ are XZ = 9√2 and YZ = 9
Which statements regarding triangle XYZ are correct?from the question, we have the following parameters that can be used in our computation:
XY = 9 cm
Also, we have the right triangle
The acute angle in the triangle is 45 degrees
This means that
XY = YZ = 9
It also means that
XZ = XY√2
So, we have
XZ = 9√2
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What is the missing number in this pattern?
1,
8,
27,
64,
125,
Answers
Answer:
1, 8, 27, 64, 125, 216, 343, 512,
How much is 1 plus 1 when adding odd numbers
Answers
The value of 1 plus 1 when adding odd numbers is 2.
What are off numbers?Odd numbers simply means the numbers that cannot be divided into pairs. They include 1, 3, 5, 7, 9, ,etc.
In this case, 1 plus 1 will be:
= 1 + 1
= 2
It's important to note that the addition of two odd numbers will give a even number.
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suppose that the mean daily viewing time of television is 8.35 hours. use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) what is the probability that a household views television between 4 and 12 hours a day? (round your answer to four decimal places.)
Answers
z1 = (4 - 8.35) / 2.5 = -1.74
z2 = (12 - 8.35) / 2.5 = 1.46
P(-1.74 < z < 1.46) = 0.8711 - 0.0428 = 0.8283
Therefore, the probability that a household views television between 4 and 12 hours a day is 0.8283 (or 82.83% when expressed as a percentage).
To find the probability that a household views television between 4 and 12 hours a day, we will use the normal probability distribution.
1. To solve this problem, we can use the normal probability distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the value we are interested in (in this case, between 4 and 12 hours), μ is the mean (8.35 hours), and σ is the standard deviation (2.5 hours).
2. We will find the Z-scores for the lower and upper bounds (4 and 12 hours, respectively) using the following formula: Z = (X - µ) / σ.
For the lower bound (4 hours):
Z1 = (4 - 8.35) / 2.5 = -1.74
For the upper bound (12 hours):
Z2 = (12 - 8.35) / 2.5 = 1.46
3. Now, we will use a Z-table or a calculator with a normal distribution function to find the probabilities corresponding to these Z-scores.
P(Z1) = P(Z < -1.74) ≈ 0.0409
P(Z2) = P(Z < 1.46) ≈ 0.9222
4. Finally, to find the probability that a household views television between 4 and 12 hours a day, subtract P(Z1) from P(Z2).
P(4 < X < 12) = P(Z2) - P(Z1) = 0.9222 - 0.0409 = 0.8813
So, the probability that a household views television between 4 and 12 hours a day is approximately 0.8813, or 88.13% (rounded to four decimal places).
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Solve the equation for all solutions in the interval. Write each answer in radians.
Answers
We are given a problem regarding trigonometric identities and asked to resolve for theta.
\(4\sec \theta-\sqrt[]{3}=\sqrt[]{3}+7\sec \theta\)Recall that:
\(\sec \theta=\frac{1}{\cos \theta}\)Therefore, we have:
\(\begin{gathered} \frac{4}{\cos\theta}-\sqrt[]{3}=\sqrt[]{3}+\frac{7}{\cos\theta} \\ \text{ We add }\sqrt[]{3}\text{ and subtract }\frac{7}{\cos\theta}\text{ from both sides to get:} \\ \frac{4}{\cos\theta}-\frac{7}{\cos\theta}=2\sqrt[]{3} \\ -\frac{3}{\cos\theta}=2\sqrt[]{3} \\ \text{Multiply both sides by }\cos \theta\text{ and divide both sides by }2\sqrt[]{3}\text{ to get:} \\ \cos \theta=-\frac{3}{2\sqrt[]{3}}=-\frac{\sqrt[]{3}}{2} \\ \theta=\cos ^{-1}(-\frac{\sqrt[]{3}}{2})=150^o \\ \end{gathered}\)In radians, we have:
\(\frac{150\pi}{180}=\frac{5\pi}{6}\)what is 7/5 as a simple thing?
Answers
In mixed number form: 1 2/5
Solve the following inequality, graph the solution on the number
line, and write the solution in interval notation.
11 − 5x ≤ − 7
Answers
The solution for the given inequality 11 - 5x ≤ -7 is x ≥ 18/5, and the interval notation is [18/5, ∞).
Solve the inequality 11 - 5x ≤ -7 and graph the solution on the number line. Also, write the solution in interval notation.
Solution : The given inequality is 11 - 5x ≤ -7To solve the inequality, we need to isolate the variable on one side of the inequality sign.11 - 5x ≤ -7-5x ≤ -7 - 11 (subtracting 11 from both sides)-5x ≤ -18
Dividing both sides by -5, we get x ≥ 18/5 The solution is x is greater than or equal to 18/5. We can represent this on the number line as follows : Interval notation for the given inequality is [18/5, ∞)
Hence, the solution for the given inequality 11 - 5x ≤ -7 is x ≥ 18/5, and the interval notation is [18/5, ∞).
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The points plotted below are on the graph of a polynomial. How many roots
of the polynomial lie between x = -4 and x = 3?
URGENT
Answers
Given:
The graph of a polynomial.
To find:
The number of roots of the polynomial lie between x = -4 and x = 3.
Solution:
From the given graph it is clear that the graph is a downward U-shaped curve. It means the given graph represents a quadratic polynomial.
The graph of the polynomial is below the x-axis immediate before x=-2 and above the x-axis immediate after x=-2. It means the graph intersect the x-axis at x=-2.
The graph of the polynomial is above the x-axis immediate before x=2 and below the x-axis immediate after x=2. It means the graph intersect the x-axis at x=2.
Since the graph of the polynomial divides the x-axis two times between x = -4 and x = 3, therefore the two roots of the polynomial lie between x = -4 and x = 3.
In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance. Find the critical value(s).
Select one:
a. Both -1.96 and 1.96
b. Only 1.699
c. Only -1.699
d. Only -1.645
e. Both -2.045 and 2.045
f. Only 1.645
Answers
In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance the critical value is 1.645. The correct answer is option f. Only 1.645.
In an upper tail test about the population mean, where the population standard deviation is known, we need to find the critical value(s) for a 5% significance level.
To find the critical value(s), we need to use the z-table. The z-table shows the probability of a z-score being less than or equal to a certain value.
Since this is an upper tail test, we need to find the z-score that corresponds to a probability of 0.95 (1 - 0.05).
Looking at the z-table, we can see that the z-score that corresponds to a probability of 0.95 is 1.645.
Therefore, the critical value for this upper tail test is 1.645. The correct answer is f. Only 1.645
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a = 10 m, b = 6 m and c = 9 m for the triangle shown below.
Work out the value of x rounded to 1 d.p.
Answers
In the given diagram, the value of x in the right triangle is approximately 14.7
Solving right triangles: Calculating the value of xFrom the question, we are to calculate the value of x in the given diagram.
In the given diagram, we have two right triangles.
First, we will calculate the value of the side joining the two triangles.
Let the side joining the two triangles be d
Thus,
From the Pythagorean theorem, we can write that
d² = a² + b²
d² = 10² + 6²
d² = 100 + 36
d² = 136
Now, in the other triangle
Also, using the Pythagorean theorem, we can write that
x² = c² + d²
x² = 9² + 136
x² = 81 + 136
x² = 217
x = √217
x = 14.7309
x ≈ 14.7
Hence, the value of x is approximately 14.7
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Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10.
Answers
Answer:
UW = 36 units
Step-by-step explanation:
The question is incomplete. Here is the complete question
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10. If UW = 9x – 9, what is UW in units?
If a point V lies between points U and W on line segment UW, then based on vector notation, UV + VW = UW.
Given parameters
The length between U and V i.e UV = 2x-4
The length between V and W i.e VW= 4x + 10.
UW = 9x – 9
Required
The length between U and W in units
Since UW = UV+VW, we will substitute the given functions into the formula as shown;
9x-9 = 2x-4+4x + 10.
9x-9 = 2x+4x-4+10
9x-9 = 6x+6
collect like terms on both sides;
9x-6x = 6+9
3x = 15
x = 15/3
x = 5
Substitute x = 5 into the function UW = 9x-9 to ge the length of UW in units.
UW = 9(5)-9
UW = 45-9
UW = 36 units
Hence the required length between line segment U and W in units is 36units.
Answer:
36 units, edge 2020-21
Step-by-step explanation:
aka D/last answer
hl meaning in geometry
Answers
Answer:
"HL" in geometry typically refers to "Hypotenuse-Leg". This term is often used when talking about right-angled triangles, where the hypotenuse is the longest side, opposite the right angle, and the legs are the two shorter sides adjacent to the right angle.
How many moles contain 1.25x 10^15 molecules of glucose
Answers
Answer:
i.e. mass of 1 mole of glucose, C6H12O6 = (6 × 12.01 + 12 × 1.01 + 6 × 16.00) g = 180.18 g (using atomic weight data to 2 decimals) 1 mole of carbon atoms weighs 12.01 g and there are 6 moles of C atoms in 1 mole of glucose, so the mass of carbon in 1 mole of glucose = 6 × 12.01 g = 72.06 g.
Step-by-step explanation:
Consider the function: h(x) = 11 - 3x What is h(-2) ?
Answers
Answer:
17
Step-by-step explanation:
11-3x
11-3(-2)
11+6
Hence, 17
Hope it helps!
The evaluation is 17 when h(-2) of h(x) = 11-3x.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co domain, and domain for every function.
The given function is
h(x) = 11-3x
when x = -2
h(-2) = 11-3(-2)
= 11 + 6
= 17.
Therefore, the h(x) = 11-3x is 17 when x = -2
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Which one could it be?
Answers
HELP!!! Find the exact value of
cos A in simplest radical form.
Answers
Answer:
cos A = 9/41
Step-by-step explanation:
cosine is a function that puts together the ADJACENT side of a triangle in a ratio with the HYPOTENUSE.
So from angle A the side length 9 is right next to A so it is the ADJACENT side. The HYPOTENUSE is the longest side ,that is the side length 41.
so cos A = ADJ/HYP
cos A = 9/41
It could be that the directions were confusing bc they said simplest radical form. Many, but not all right triangles have one or more sidesides that have a radical as part of their measure. This triangle doesn't. If you get a radical in the denominator of a ratio, be sure to rationalize so that there is no radical on the bottom.
. Seiji and Gavin both worked hard over the summer. Together they earned a total of $425. Gavin earned $25more than Seiji.
(a) Write a system of equations for the situation. Use s for the amount Seiji earned and g for the amount
Gavin earned.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each person earned.
I need help with b
Answers
Answer: b
Step-by-step explanation:
Its not right im doing this for point
EASY 7TH GRADE MATH! FIRST PERSON MARKED BRAINLIEST, NEED HELP NOW!!!
Answers
Answer:
slope of 2 and y-intercept of 1
(3rd answer choice)
Step-by-step explanation:
Answer:
It's the last one doesn't matter which way you go they are both going to the negative way because they are going down and to the left so they are both negative. I hope this helps good luck.
the true length of boards at a cut mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. what proportion of the boards will be greater than 122 inches? 50% 84% 68% 34%
Answers
The proportion of the boards that will be greater than 122 inches is 84%
Given :
length of boards is listed as 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.
we are aske to determine what proportion of the boards will be greater than 122 inches = ?
we have :
μ = 123
σ = 122
now, let x denote the number of boards.
⇒ X ∼N (μₓ , σₓ²) X∼N(123,1)
⇒ P(X>122)=P( X- μₓ/ σₓ > 122-123/1)
⇒ P(Z > -1)
= 0.08413
= 84%
hence we get the value as 84%
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exact differential equation (x siny)dx (xcosy-2y)dy=0
Answers
The general solution to the exact differential equation (x sin y)dx + (x cos y - 2y)dy = 0 is (1/2)x² sin y - y² = C.
Now, let's examine the given equation. We need to check if there exists a function f(x,y) such that df = (x sin y)dx + (x cos y - 2y)dy. In order for this to be true, we must have:
∂f/∂x = x sin y
and
∂f/∂y = x cos y - 2y
Taking the partial derivative of the first equation with respect to y gives:
∂²f/∂y∂x = cos y
And taking the partial derivative of the second equation with respect to x gives:
∂²f/∂x∂y = cos y
Since the second partial derivative with respect to x and y are equal, we can say that the equation is exact.
Now that we know the equation is exact, we can find f(x,y) by integrating the first equation with respect to x and the second equation with respect to y. Integrating the first equation gives:
f(x,y) = ∫(x sin y)dx = (1/2)x² sin y + g(y)
Where g(y) is a constant of integration that depends only on y.
Now we need to differentiate this equation with respect to y and set it equal to the second equation. Differentiating with respect to y gives:
∂f/∂y = x cos y + g'(y)
Setting this equal to x cos y - 2y, we can solve for g'(y):
g'(y) = -2y
Integrating g'(y) gives:
g(y) = -y² + C
Where C is a constant of integration.
Putting this all together, we get:
f(x,y) = (1/2)x² sin y - y² + C
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Write the fraction below as a sum or difference. 5x + 2 over 7
Answers
Answer:
f ^-1 (x) =7X/5 - 2/5
Step-by-step explanation:
David traveled 4/5 of his trip by bicycle and the rest of the distance by foot. If the whole trip was 160km, how many kilometres dad he travel by foot?
Answers
Answer:
Step-by-step explanation:
I will explain it in a screenshot. That all the way is divided into 5 parts. And 4 of them were by bicycle, and 1 part is by walk. So we divide all the way to 5 and multiply to leftover 1 piece.
Ryan has a semicircular garden as shown.
What is the distance around his garden in feet? Use 3.14 for 7.
Enter the correct answer in the box.
ft
Answers
894
yiufkutfluy.clutkyskdtuf,yjhktgnf,juyigcjuhfgyiuchfyjubkg
Answer:
i think it would be around 34 feet
Step-by-step explanation:
the bottom is cut in half and each half is 8 and 1/2 feet so if you add 8 and 1/2 + 8 and 1/2 you would get 17 and then the top is rounded so you would just add 17 and 27 together to get the distance around.
Select all equations that can represent the question: "How many groups of 45 are in 1?" A ?⋅1=45? Times 1 is equal to 4 fifths B 1⋅45=?1 times 4 fifths is equal to ? C 45÷1=?4 fifths divided by 1 is equal to ? D ?⋅45=1? Times 4 fifths is equal to 1 E 1÷45=?1 divided by 4 fifths is equal to ?
Answers
This question is not correctly written.
Complete Question
Select all equations that can represent the question: "How many groups of 4/5 are in 1?" A ?⋅1=4/5? Times 1 is equal to 4 fifths B 1⋅4/5=?1 times 4 fifths is equal to ? C 4/5÷1=?4 fifths divided by 1 is equal to ? D ?⋅4/5=1? Times 4 fifths is equal to 1 E 1÷4/5=?1 divided by 4 fifths is equal to ?
Answer:
D ?⋅4/5=1 = ? Times 4 fifths is equal to
E 1÷4/5=? = 1 divided by 4 fifths is equal to
Step-by-step explanation:
How many groups of 4/5 are in 1?
The operation used to solve this is that Division operation.
Hence, we solve it by saying:
1 ÷ 4/5 = ?
= 1× 5/4 = ?
5/4 = ?
Cross Multiply
5 = 4 × ?
? = 5/4
The equations that can represent the question: is
Option D ?⋅4/5=1 = ? Times 4 fifths is equal to
Option E 1÷4/5=? = 1 divided by 4 fifths is equal to
The points X, Y, and Z are on the same directed line segment XYZ. The ratio of XY:XZ is 2:3. If point X is located at (6,10) and point Y is located at (-1,8), what are the coordinates of point Z?
Answers
The coordinates of Z are (-11.5, 5)
What is section formula?When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = (m\(x_2\) + n \(x_1\) / m+ n, m \(y_2\) +n\(y_1\) /m+ n)
Given coordinates:
XY:XZ is 2:3
X is located at (6,10) and Y is located at (-1,8).
let the coordinates of Z(x, y)
using section formula
-1 = (2x + 18)/ 5
-5 = 2x +18
2x = -23
x= -11.5
and, 8 = 2y + 30 /5
40 = 2y + 30
2y= 10
y=5
Hence, the coordinates of Z are (-11.5, 5)
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