Evaluate the following integrals. 1. S 1- coth² (log2 x) x cosh(log₂ x) -dx π 3 (sin³ x) VT (sin³x)√1 + cos x dx 2.

Q: Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field,…

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Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: Q1: Solve the following PED: ди ди = дı ?x² ; if u (x, 0) = 2x when 05x5 05x52

A: Note:- These are multiple questions and according to our company guidelinne we can do maximum 1…

Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: 5. Find the area bounded by y = sin √x and y = 0 on the interval [0, π²].

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Q: Consider the function f(x) = 7x² - 6x² - 6. Identify the locations where f has transition points,…

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Q: Given that -3 9+x² following functions: (-1)n+1 32n+1 4x (9+x²)² Σn=0 2. g(x) = x2n. Obtain the…

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Q: Can you solve this and show work clearly, the first part is X to the 3

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Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

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Q: e each limit. If the limit does not exist, e 2 3 4 5 →

A: We have to find the following conditions according to the given information

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: 4. (x³ − 2x² + 1)dx [³ (x² - 2x + 5)²

A: The integral to be evaluated is ∫x3-2x2+1dxx2-2x+52. The first step will be to do a partial fraction…

Q: 9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that…

A: The given function is  Q(x)=cos9(4x-5).

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: (a) For a certain curve, y"=2. Find its equation given that it passes through P(2, 6) with slope 10.…

A: Note: according to the company policy we can attempt only one question so please upload the next…

Q: Show that, given the three angles A, B, and C of a triangle and one side, say a, the area o the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: I. Directions: Determine if the function is continuous on the given interval 1-3. f(x) 2 12-x² ; [1,…

A: 1. fx=212-x2; 1,32. fx=2-x+3; -3,-13. fx=1if x≤2x2-3if x>2; 2,4

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

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Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: This question can be solved using the concept of maxima and minima.

Q: Perform the integration. (sinh x)(coth? x + csch3x) dx

A: Here is the solution:

Q: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: Perform the integration. π ¹3 sec³ x tan x dx √2 + secx 0

A: A detailed solution is given below.

Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

A: Center of gravity is given.

Q: Evaluate 2y"+3y'-2y-te-2t ,y(0)=0, y'(0)=-2

A: answer is in next step. please give a like !!

Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

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Q: II. Evaluate the following integrals. 2. (sin³x)√1 + cos x dx KIN k 플

A: Here is the solution:

Q: Life expectancy in the United States has been rising since the nineteenth century. The table shows…

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Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: Question 138 of 190 FINAL-Mathematics Temperatures in degrees Celsius (C) may be changed to degrees…

A: A detailed solution is given below.

Q: 4. The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

A: answer is in next step.  please give a like !!!!

Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, R'(x)=(x+2)ln(x+2)

Q: Convert the degree measure to radian measure. Round to three decimal places. −46.23°

A: Convert the degree measure to radian measure. Round to three decimal places. −46.23°   Please show…

Q: The human population of Earth in July 2014 was 7.295 billion, and was expected to grow by about…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: The solid generated by x+y=5, y=0 and x=0, about y=0

Q: Solve the non-homogeneous linear recurrence relation. (note: the non-homogeneous part is a constant…

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Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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Q: The joint cost (in dollars) for two products is given by C(x, y) = 24 + x² + 3y + 2xy where x…

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Q: 3. coth 3x dx

A: To evaluate the integral.

Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A: Using sine rule, length of other two side are evaluated.

Q: Using the Ring or Washer method, what will be the equation of the volume of the solid formed when…

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Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

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Q: Sketch the graph of r = 0 90° +2

A: To sketch the graph of r=θ90°+2.

Q: Suppose that $2,500 is deposited into an account paying 6.2% interest compounded continuously.…

A: $2,500 is deposited into an account paying 6.2% interest compounded continuously.

Q: A farmer wants to fence an area of 6 million Square feet in a rectangular field and a divided in…

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Q: The height of a projectile launched into the air is given by f(t)= - 16t² + 220t + 10, where t is…

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: Given f(x) = x^5 * cos x, dx= 0.01, use numerical differentiation to find: (1) df/dx for this…

A: Concept: The formula for the differentiation of the product of two function Let the two functions be…

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

A: We will use partial derivative to find x and y.