[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{ - 1} t \: dt}[/tex]
Answers
Use L'Hopital's rule twice:
[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \lim_{x\to0^+} \frac1{\sin^2(x)} \left(\int_0^x \sin^{-1}(t) \, dt - \int_0^{\frac x2} \sin^{-1}(t) \, dt\right) \\\\ = \lim_{x\to0^+} \frac{\sin^{-1}(x) - \frac12 \sin^{-1}\left(\frac x2\right)}{2\sin(x)\cos(x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{2\sin^{-1}(x) - \sin^{-1}\left(\frac x2\right)}{2\sin(2x)} \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{2\sqrt{1-\frac{x^2}4}}}{4\cos(2x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{\sqrt{4-x^2}}}{4\cos(2x)}[/tex]
The remaining limand is continuous at x = 0, and the limit is
[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \frac{2-\frac12}4 = \boxed{\frac38}[/tex]
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/Oc1eIaAqjbs8KCnGaLZZVKUhnF5QHact.jpeg)
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/LvBteEcmZIJaQI3hpKLwM4parnGiRnu8.jpeg)
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/leifCbR0Yn68TY0MVRLAYZE7TAQAJCTL.jpeg)
Related Questions
Simplify the expression. Write the answer using scientific notation.
A)2.52 × 10–3
B)2.52 × 10–2
C)2.52 × 10–1
D)4.3 × 10–2
Answers
Answer:
B.
[tex]2.52 \times 10 ^{ - 2} [/tex]
Brainlisted for the correct answer! Need help due today!
Answers
Answer:
a. 21.95 or abt 22
b. Length of the ladder
Step-by-step explanation:
pythagorean theorem - a^2 + b^2 = c^2
[c is slope/hypoteneuse] [a and b are sides]
11^2 + 19^2 = c^2
121 + 361 = c^2
482 = c^2
sqrt(482) = c
c = 21.954 or abt 22
If you deposit $300 in an account and it grows by 6% each year, how much money will be in your account after 1 year?
Answers
Answer:
318
Step-by-step explanation:
300 + (300 * 6%) = Answer
300 + (300 * 0.06) = 318
A cylinder has a diameter of 10 decimeters. What is the length of the curved surface?
78.5 decimeters
31.4 decimeters
62.8 decimeters
15.7 decimeters
Answers
Length of curved surface = 2π x 5 = 10π ≈ 31.4 decimeters.
Cual es la formula para calcular la masa de los atomos de carbono y nitrogeno?
POR FAVOR Y DOY CORONA Y CORAZON
Answers
Answer:
La masa atómica del carbono (C) es 12 g/mol; para el oxígeno (O) es de 16 g/mol. Esto significa que 6.022 x 1023 átomos de carbono pesan 12 gramos. Según esto, el peso molecular del CO2 es: 12 g/mol [C] + 2 x 16 g/mol [O2] = 44 g/mol.
1 molécula de Nitrógeno por su masa atómica de 14.01 más 3 moléculas de Hidrógeno por su masa atómica de 1.008 = (1 * 14.01) + (3 * 1.008) = 14.01 + 3.024 = 43.038 u = 17.03 masa molecular = 17.03 g/mol de masa molar en el amoníaco.
Mr. Alden Richards is planning to build a gazeboo whose base is a regular octadecagon. At what angle should he cut the lumber to frame the base.
Answers
Answer: Set your blade tilt to 67.5 degrees.
I really need help with this
I will check to see if it right before giving points thank you.
Answers
Step-by-step explanation:
For the question question, since they are giving you the function you just need to find the input that matches the expected output (y) which will be the number of miles biked. So what numbers multiplied by 12 give you 12, 36, and 48?
You could substitute y into an algebraic function to find these values.
We'll use 36 miles as an example.
If 12x = y then
12x = 36
divide both sides by 12
x = 3
For the second question you are given the x value (number of guests) and just need to calculate y (cupcakes each guest is allowed) by dividing 30 by the number of guests (x).
Suppose A and B are independent events. The probability that event A will not occur is 0.1 and the probability that event B will occur is 0.7. Find P(A), P(not B) and P(A and B).
Answers
Answer:
The probability for A is 1-0.1 is 90%
P(A)=90%
P(NOT B)=30%
P(A AND B)=0.9+0.7/2=1.6/2=80%
p(a and b) may be a little off.
Answers:
P(A) = 0.9P(not B) = 0.3P(A and B) = 0.63=======================================================
Work Shown:
P(A) = 1 - P(not A)
P(A) = 1 - 0.1
P(A) = 0.9
-------------------
P(not B) = 1 - P(B)
P(not B) = 1 -0.7
P(not B) = 0.3
-------------------
P(A and B) = P(A)*P(B) only when A and B are independent
P(A and B) = 0.9*0.7
P(A and B) = 0.63
Find the area of the polygon
Answers
Answer:
810 m
Step-by-step explanation:
Split the polygon into two parts
(Small and Big rectangle)
SR : 18(18+3) = 378
BR : 18(3+3+18) = 432
378+432 = 810
Hope this helps :)
What was her speed?
0.1 mile per minute
0.5 mile per minute
5 miles per minute
10 miles per minute
Answers
Answer:
0.1 mile per minute
( option A )
helppppppp!!!!!!!!!!!!!!
Answers
Answer:
20 oz
Step-by-step explanation:
12 + 20 = 32
32 to 20 is equal to 8 to 5
I NEED HELP ASAP I WILL GIVE BRAINLY~
Answers
Answer:
x + 5
Step-by-step explanation:
i think
A taxi company charges a flat fee of $3.50 per ride plus an additional $0.65 per mile. If Ian has only $10, what is the farthest he can ride?
Answers
Answer:
10 miles
Step-by-step explanation:
Before he goes anywhere there is a fee of $3.50. $10 - $3.50 = $6.50. If you divide $6.50 by $0.65 you can find how many miles he can ride. $6.50 divided by $0.65 = 10. That means Ian can ride the taxi for 10 miles.
2x+2=4 solve for x please help me solve this problem
Answers
Answer:
x = 1
Step-by-step explanation:
First subtract 2 on both sides.
2x + 2 -2 = 4 - 2
2x = 2
Divide by 2 on both sides
2x/2 = 2/2
x = 1
Answer:
x=1
Step-by-step explanation:
cause it do 2 multiplied by 1 is 2 plus 2 is 4
HELPPPPPPPPPPPPPPPPPPPPPPp
Answers
Answer:
162
Step-by-step explanation:
to find the surface area of the rectangles do base x height
5 x 10 = 50
there are 3 sides on a triangle so do 50 x 3 = 150
now we need to find the area of the triangles
the formula for the surface area would be base x height ÷ 2
3 x 4 = 12
12 ÷ 2 is 6
because there are 2 triangles you would need to multiply it by 2
6 x 2 is 12
add it all together
12 + 150 is 162
Evaluate the following integrals
Answers
Answer:
[tex] I = \frac{1}{8} e^{4x^2} + C [/tex]
Step-by-step explanation:
This can be solved using substitution method. Let us work it out.
[tex] Let \: I = \int xe^{4x^2} dx[/tex]
[tex] \implies \: I = \int e^{4x^2} xdx[/tex]
[tex] Put \:4x^2 = t [/tex]
[tex] \implies 8x dx = dt [/tex]
[tex] \implies x dx = \frac{1}{8}dt [/tex]
[tex] \implies \: I = \int e^{t} \frac{1}{8}dt [/tex]
[tex] \implies \: I = \frac{1}{8} \int e^{t}dt [/tex]
[tex] \implies \: I = \frac{1}{8} e^{t} + C [/tex]
[tex] \implies \: I = \frac{1}{8} e^{4x^2} + C [/tex]
[tex] \implies \: \int xe^{4x^2} dx = \frac{1}{8} e^{4x^2} + C [/tex]
The elevation of Death Valley is -86 meters. Which equation shows how many meters below sea level Death Valley is located? Group of answer choices |-86| = 86 |-86| = - 86 |86| = -86 |86| = 86
Answers
Answer:
|-86| = 86
The absolute value of -86 is 86!
Tip : The absolute value is always positive.
Answer:
|-86| = 86
Step-by-step explanation:
The time to complete a project varies inversely with the number of employees. If 6 people can complete the project in 4 days, how long will it take 8 people?
Answers
Answer:
3 days
Step-by-step explanation:
A random sample of 1400 home owners in a particular city found 644 home owners who had a swimming pool in their backyard. Find a 95% confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard
Answers
Last year, Handy Hardware
Store sold 45,078 bolts and
5,011,542 nails. How many more
nails did the store sell than bolts?
Answers
Answer:
5,011,542 nails - 45,078 bolts = 4,966,464 more nails sold than bolts
Step-by-step explanation:
What is entrepreneurial finance?
Answers
Answer:
The process of making financial decisions for new ventures (i.e. startups). New ventures are inherently different from established ventures, as are entrepreneurs inherently different from conventional business managers.
4. Jorge has a mass of 45 kilograms and
is skateboarding with a velocity of
3 meters/second north. What is Jorge's
momentum? The units for momentum are
kg-m/s north.
Answers
Jorge's momentum given his mass and the velocity while skateboarding is 135kg-m/s north.
What is momentum?Momentum can be described as the impetus that is gained by an object that is motion. Momentum is velocity multiplied by mass. When put simply, momentum can be described as mass in motion. Thus, when an object is moving, it has momentum.
Momentum velocity x mass
45 x 3 = 135kg-m/s north.
To learn more about momentum, please check: https://brainly.com/question/24030570
an athletic director pays $90 for 12 visors, how much will the athletic director pay to buy 15 visors?
Answers
Answer:
sample What is the length of a rectangle if the width is
10 centimeters and the diagonal is 16 centimeters?
Step-by-step explanation:
7.5 x 15 is 112.50
The athletic director will pay $112.50 for 15 visors. Hope this helps and please mark brainliest!
answer please hfghfg
Answers
Answer:
it is D 6 x 10,000+3x 1000+9 x100 +1 x10 +4 x1 +2 x0.1 +5 x0.01
Step-by-step explanation:
hope this helps pls makes as brainliest
I WILL GIVE BRAINLIEST + 25 POINTS PLEASE HELP
Answers
Answer:
25
Step-by-step explanation:
Answer:
50.24 square yards
Step-by-step explanation:
Area of the circle
A = πr²A = 3.14 x (4)²A = 3.14 x 16A = 50.24 square yardsHELP ASAP!!!
This circle is centered at the origin, and the length of its radius is 3. What is
the circle's equation?
A. x + y3 = 27
B. x² + 7 = 9
c. x² + 7 = 3
D. x+y = 3
Answers
Which expression is equivalent to the expression shown below?
-9.25(2n-3) - 8n
A. -18.5n + 19.75
B. 55.5n+ 27.75
C. 26.5n + 19.75
D. 27.75 -26.5n
Answers
Answer:
option D
Step-by-step explanation:
Distribute (-9.25) to 2n and (-3). When we multiply (-9.25) and 2n, we get -18.5n and when we multiply (-9.25) and (-3) we get 27.75.
-9.25(2n - 3) - 8n = -9.25*2n - (-9.25) *3 - 8n
= -18.50n + 27.75 -8n
= -18.5n - 8n + 27.75
Combine like terms. Here (-18.5n) and (-8n) are like terms
= -26.5n + 27.75
Find b given to that a= 20 angle a= 30 degrees and angle b = 45 degrees in triangle abc
Answers
Answer:
Step-by-step explanation:
Select the best answer for the question.
15. If the following fractions were converted to decimals, which one would result in
O A.314
O B.5111
O C.317
OD. 1/9
Answers
Upon asking I got the rest of the information needed to answer this question.
-> Which one becomes a repeating decimal?
Your answer is D. 1/9.
1/9 = 0.111111111111111111111111111111111 ... or 0.1 repeating. It can be written with a line over the 1 asyou can see in the attached.
This means that D is the answer to your question.
Trudie is playing a game with identical-sized colored sticks. She has a container with a total of 10 red, 12 green, 19 blue, and 9 yellow sticks.
If Trudie picks a stick without looking, what is the probability the stick will be green?
A 12%
B 24%
C 76%
D 88%
Answers
Answer:
B. 24%
Step-by-step explanation:
Filling the character requirement lol
Answer:
b
Step-by-step explanation:
it gies in and out the equation