Use fundamental theorem of calculus to find derivative of the function LOOK AT PHOTO
Answers
Let c > 0. Then split the integral at t = c to write
\(f(x) = \displaystyle \int_{\ln(x)}^{\frac1x} (t + \sin(t)) \, dt = \int_c^{\frac1x} (t + \sin(t)) \, dt - \int_c^{\ln(x)} (t + \sin(t)) \, dt\)
By the FTC, the derivative is
\(\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}\)
Related Questions
what is the answer for 6x + 3(x-2)
Answers
Answer:
9x - 6
Hope this helps! <3
(If you need a step by step lmk)
Answer:
6x+3(x-2)
6x+3x-6
9x-6
Please help me it's very hard
Answers
B. No Solution
What has no solutions in common with 6x+2y=12
Answers
Answer:
-6x - 2y = 12
Step-by-step explanation:
Which set of ordered pairs (x, y) could represent a linear function?
A = {(-8,8), (-4,5), (0, 2), (5, -1)}
B = {(-1, -2), (2,1), (5,4), (8,7)}
C = {(-2,8), (1,5), (4,2), (6, -1)}
D = {(-1,0), (1, 1), (7,5), (9,6)}
Answers
The ordered pairs that represent the linear function is Option A, B and C.
What is linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.
To determine which ordered pairs represent a linear function we use the equation of slope.
The slope is given as:
m = (y2 - y1) / (x2 - x1)
Option A:
m = (5 - 8) / (-4 + 8) = -3 / 4
m = (2 - 5) / (0 + 4) = -3/ 4
The slopes between the consecutive points are same hence option A represents a linear equation.
Similarly, for option B:
m = (1 + 2) / (2 + 1) = 1
m = (4 - 1) / (5 - 2) = 1
Option B is correct.
Option C:
m = (5 - 8) / (1 + 2) = -3 / 3 = -1
m = (2 - 5)/ (4 - 1) = -1
Option C is correct.
Option D:
m = (1- 0)/ (1 + 1) = 1/2
m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3
Option D is incorrect.
Hence, the ordered pairs that represent the linear function is Option A, B and C.
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Smallest successive composites with gap
17, 73, 2, 19
Answers
Answer:
Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:
1. $341 = 11 \times 31$
2. $458 = 2 \times 299$
3. $460 = 2^2 \times 5 \times 23$
4. $479 = 13 \times 37$
I’ll give brainliest
Answers
Opposite: 90 - 58 = 32
180 - 32 = 148
Please Rate Helpful & Or Brainlyest! Hope this helped!
Answer:
oh delete my answer ;-;
Step-by-step explanation:
You deposit $1000 into an account that pays interest compounded monthly. What interest rate do you need to double your money in 10 years? (as a percent, so change it back, write to two decimal places)
Answers
The interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
How did we get the value?To calculate the interest rate required to double your money in 10 years with monthly compounding, you can use the formula:
rate = ( (2 * principal) / principal * (1 + n)^(t12) )^(1/t12) - 1
where
principal = $1000
t = 10 years
n = number of compounding periods per year (12 for monthly compounding)
Plugging in the values we get:
rate = ( (2 * 1000) / 1000 * (1 + 12)^(1012) )^(1/1012) - 1
rate = ( 2 * (1 + 12)^120 )^(1/120) - 1
rate = ( 2 * 169860981.54 )^(1/120) - 1
rate = 1.3327
So, the interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
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This is due today pls answer
This table shows the heights of some of the tallest buildings in the United States. Use the table to answer the question.
If the Willis Tower and the Empire State Building were stood end to end, how high would they reach?
Answers
Answer:
2,700 ft in the air
Step-by-step explanation:
what is the ratio of 1:2:4 multiply by 70
Answers
Answer:
0.125 is the answer (I don't know step by step)
ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
Answers
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
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his question is about filling in the blanks in the derivation of the first and second barycentric interpolation formulas. recall that the j-th lagrange polynomial is defined as
Answers
A variation on Lagrange polynomial interpolation is called barycentric interpolation. Second, just use Newton interpolation formula to assess p(x) for each x.
Why is the Lagrange interpolation theorem important?The Lagrange interpolation theorem can be used to create a polynomial that traverses a specified set of points and takes particular values at random locations. This theorem provides the approximate formula for the nth degree polynomials to the function f if a variable f (x) is available at discrete places xi, I = 0, 1, 2,... (x).
What is the LaGrange theorem's conclusion?The Lagrange theorem extrapolates well-known mathematical principles like the statement that a line is uniquely specified by two points, the knowledge that the quadratic function polynomial is completely determined by three points, and so forth.
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simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answers
Answer:
-12+28i+3i-7i-65i+28
14 -41i
WILL MAKE BRAINLIEST! ANSWER AND ILY
what are the slopes of each line?
Answers
Answer:
Top left is A
Top right is B
Bottom left is D
Bottom right is A
Step-by-step explanation:
7.) A. Undefined
8.) B. 0
9.) D. -1/2
10.) A. -2/5
Find an equation of the sphere that passes through the point (6, -2, 3) and has center (-1, 2, 1). Find the curve in which the sphere intersects the yz-plane. Find the center and radius of the sphere
X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0
Answers
Answer:
A) x^2 + 2x+ y^2 - 4y + z^2 - 2z - 63 = 0
B) radius = 5
center = (4,-1,-3)
Step-by-step explanation:
\(x^2 + y^2 + z^2 - 8x + 2y + 6z + 1 = 0\)
A ) Determine the curve in which the sphere intersects the yz-plane
determine the radius ( r ) = √((6-(-1))2+(-2-2)2+(3-1)2) = √69
next the equation of the sphere ( curve in which the sphere intersects the yz-plane )
x^2+2x+y^2-4y+z^2-2z-63 = 0
B) determine the center and radius of the sphere
X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0
(x-4)2+(y+1)2+(z+3)2 = 25 = 52
radius = 5
center = (4,-1,-3)
A swimming pool 30 feet long and 20 feet wide is surrounded by a deck that is 5 feet 6 inches wide. What is the area of the deck in square feet?
Answers
Answer:600?
Step-by-step explanation:
find the missing value 1/2 equals 28 over X
Answers
Answer:
x = 56
Step-by-step explanation:
cross multiply. 28 times 2 and 1 times x. set them equal to each other and solve for x to get 56.
H(p)=p/5 + 15
What is the independent variable in this function
Answers
In the given function H(p) = p/5 + 15, the independent variable is "p" ,
The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.
It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.
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Planes T and X are parallel. Plane T contains line a. Plane X contains line b.
Planes T and X are parallel. Plane T contains line a and plane X contains line b.
Which best explains the relationship between lines a and b?
Answers
Someone help please
Answers
Answer:
X , XZ , Z , XY , Y , ZY , ZYX
Step-by-step explanation:
answer left to right
Pleasee finding the letters in angles
Answers
The diagram shows a cylinder of radius 6 units and height 10 units.
Which of the following gives the best ESTIMATE for the curved (lateral) surface area of the cylinder?
Please answer quick because I might leave any minute?
Question 13 options:
a. 240
b. 350
c. 380
d.280
Answers
2(2q + 1.5) = 18 - 9
Answers
Answer:
q= 1,5
Step-by-step explanation:
hope it helps...
A honeybee colony that contains 50,000 bees in late fall
may have only 10,000 bees at the end of winter. What
percent of the bees live through the winter season?
a. 5%
b. 20%
c. 25%
d. 50%
Answers
Answer:
The answer is B. 20%
Step-by-step explanation:
50,000×0.20= 10,000
10,000÷50,000= 0.20
0.2= 20%
Given:
Number of bees in late fall = 50,000 bees
Number of bees after winter = 10,000 bees
To find:
Percent of bees that live through winter
Steps:
To find the percent of bees that live through winter,
percent of bees that live through winter = \(\frac{Number 'of' bees' after' winter}{Number 'of' bees' in' late 'fall}*100\)
= \(\frac{10,000}{50,000}*100\)
= \(\frac{1}{5}*100\) (the zeros get canceled out)
= \(\frac{100}{5}\)
= 20%
Therefore only b) 20% of bees survive through winter.
Happy to help :)
If you need any help, pls feel free to ask
Solve for x : 10x-8= 4-6x
anyone help?
Answers
Answer: x = 3
Step-by-step explanation:
Simplifying
10x + -4 = 6x + 8
Reorder the terms:
-4 + 10x = 6x + 8
Reorder the terms:
-4 + 10x = 8 + 6x
Solving
-4 + 10x = 8 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
-4 + 10x + -6x = 8 + 6x + -6x
Combine like terms: 10x + -6x = 4x
-4 + 4x = 8 + 6x + -6x
Combine like terms: 6x + -6x = 0
-4 + 4x = 8 + 0
-4 + 4x = 8
Add '4' to each side of the equation.
-4 + 4 + 4x = 8 + 4
Combine like terms: -4 + 4 = 0
0 + 4x = 8 + 4
4x = 8 + 4
Combine like terms: 8 + 4 = 12
4x = 12
Divide each side by '4'.
x = 3
Simplifying
x = 3
Add
to both sides of the equation
Simplify
Add
to both sides of the equation
Simplify
6
Divide both sides of the equation by the same term
10. Higher Order Thinking Each of 5 friends has x action figures in
his or her collection. Each friend buys 11 more action figures. Now
the 5 friends have a total of 120 action figures.
a. Write an equation that models the problem.
b. Solve the equation to find the number of action figures, x, that
each friend had originally.
Answers
Each friend had originally 13 action figures before buying 11 more.
Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.
a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.
Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.
The total number of action figures will be 5(x + 11) = 5x + 55.
Now, according to the problem,5x + 55 = 120
This is our equation that models the problem.
b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.
5x + 55 = 120
5x = 120 - 55 (subtract 55 from both sides)
5x = 65x = 13
Therefore, each friend had originally 13 action figures before buying 11 more.
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Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?
Answers
Answer:
Step-by-step explanation:
Today's Age = 30
Retirement Age = 64
Total Monthly Deposits = ( 64 - 30 ) * 12 = 408
In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%
Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%
Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )
= $100,000 * 7.4864
= $748,642.20
Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )
= $1,000,000 * 0.050535
= $50,534.52
Now the Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52
= $799,176.70
Now the monthly deposit be X
= X * FVAF ( 408 , 1% ) = $799,176.70
= X * 5752.85 = $799,176.70
X = $138.918
Therefore Monthly Deposit = $138.92
Which graph represents the following piecewise defined function?
(-2x, X<-2
g(x) = -x?, -2
w
X, XZ1
5
01
3
(3.2)
(-4,2)
2
1
o
6 5 4 3 2
→
2. 3 4 5 6 x
(1.-1)
-2
-3+
ๆ ๆ
(-2,-4)
-5
6
Answers
A piecewise function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. The piecewise function is attached below.
What is a function?A function is an expression used to show the relationship between two or more numbers and variables. A piecewise function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
Given the following piecewise function, the graph is attached below.
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Answer:
x², x<0
1 g(x)= x, 0<x<4 2
X, X>4
Step-by-step explanation:
c
A man makes a cuboid of moulding clay of dimension.12cm,9cm,8 cm respectively.to make a perfect cube how many such cuboid are required
Answers
Answer:
72 such cuboids are required to make a perfect cube.
Step-by-step explanation:
V = l x w x h
V = 12 cm x 9 cm x 8 cm = 864 cm^3
edge length = V^(1/3) = (864 cm^3)^(1/3) = 12 cm
V_cube = edge length^3 = 12 cm^3
number of cubes = V_cuboid / V_cube = 864 cm^3 / 12 cm^3 = 72
Therefore, 72 such cuboids are required to make a perfect cube.
Use a significance level of α= 0.05 and use the given information for the following:
Required:
a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Answers
"we dont gaf abt no bii, we dont giveeaf abt no bii and if i was you i wouldnt kiss her on the lips"
need help asap!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: I haven’t done this in a bit, but I think this is right.
Step-by-step explanation:
