Test for exactness then solve. (6x + y2)dx + y(2x − 3y)dy = 0

Q: y s 5 4 -2 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y = x…

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Q: S 2sin(4x +9)dx

A: Given query is to find the integral.

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y^2 = x…

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Q: [*(sin³r)√1 + cos ar dr x

A: We know that integration power rule is given as  Integration of xn is xn+1/n+1.   Here i attached…

Q: 3. Σ7ne-² (Integral Test) n=1

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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: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the production for minimum average cost.

Q: 3. coth 3x dx

A: To evaluate the integral.

Q: 5. Find the area bounded by the parabola y = x^2 - 3 and the line y =1.

A: Given problem:- Find the area bounded by the parabola y = x2 - 3 and the line y = 1 .

Q: dy dx = x+1 2(y+3)

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Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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

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Q: Question 4 Given a second order differential equation d²x dx 2 + 10x = e²t dt² dt dx where t = 0, x…

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Q: What is the x-coordinate of the centroid of the plane region bounded by the x-axis and the…

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Q: Evaluate fx² cosh x dx

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Q: S 1 V1 + v 2

A: We have to find integral

Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: The integral of 3^4x dx is equal to * O 4^4x / In3 + C O 3^4x/In12 + C O 3^4x / In27 + C O 3^4x /…

A: SOLUTION-

Q: V. Directions: Find the extreme values of the given functions within the indicate 42-44. ƒ (x) = x²…

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Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 + 1.…

A: Here, the region bounded by the curves y=x2+1, y-axis , x-axis & x=2 is: which is rotated…

Q: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: equences . Given that a₂ = 6 and as 96 are terms of a geometric sequence, find a. 2. Given that a10…

A: solution

Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Compute ff 24xyd A where R is the region bounded by R x = 1, x = 2, y = x, y = x².

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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: Please graph the function of D(t)= 28sin(360/365 t - 1.4)

A: Let's graph the given function.

Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: 4. Which of the following lines is parallel to y = 6x 18? 3x+6y=2 ○ 2x + 3y = −2 -6x -6x - 2y 2y =…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Given :y=9-2x0<y<8revolution about y-axis

Q: Evaluate S2² (2x + 3e* − ¹) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given :∫122x+3ex-4xdx

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: Question Eight y s 8 7 5 4 14 4 3 -2 -1 The diagram shows the shaded region bounded by the curves y…

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Q: 12. We have the following width measurements of 80 meters wide lake Distance: 0 10 20 30 40 50 60 70…

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Q: In Dollars Sales Monthly 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 January Williams Custom…

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Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

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.

Q: IV. Directions: Find the derivative of the following functions. x²+³√x+√x+28 22-26. f(x) = VX 27-31.…

A: We have to find derivative

Q: II. Directions: Find the slope of the line tangent to the given curve at the indicated point 10-12.…

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Q: What is the y = x^3 and y = x^2? O2/5 3/5 6/35 12/35 y-coordinate of the centroid of the plane…

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Q: In a certain country, the number of people who drive electric vehicles can be mod the function P(t)…

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Q: Find the volume of the sould generated by revolving the area bounded by the _given curves about the…

A: Let's find volume of solid (V) = ?

Q: 1-10 J = exp(-x²)dx 0 Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1

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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: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A: A particle is moving along a horizontal line such that its velocity in m/s is given by vt=2t2-16t+30…

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

A: A detailed solution is given below.