Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

Q: 5. I. Evaluate each determinant. 2 -2 4 L

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Q: 3. y= x²-3x-4 x+2

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Q: a. y = 3et-2 et +1

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Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: The line passing through the points 1,3,0 and 2,4,4

Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: 2. -4 1 3 -3

A: to evaluate: -431-3

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Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. True…

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Q: Find all solutions of the equation 2 sin² x - COS X = 1 in the interval [0, 2π) with x₁ < x2 < x3.…

A: The given equation is: 2sin2x-cosx=1 To find the solution in the interval [0,2π).

Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We state Divergence Theorem and explain it.

Q: x4 Lz²+9dx 3x³ +9x−27 tan- ¹ (-) +C Option 1 x³ − 9x + 27 tan−¹ (3) + C Option 3 3x³ + 9x 9x + 27…

A: Here Is the solution

Q: (a) Solve the first order linear ordinary differential equation x sin x + (sin x + x cos x) y = xe…

A: As per bartleby guidelines we only give first question answers.

Q: Given the triangle to 4 decimal places. x = 26/ 42° 28 x find the length of side x using the Law of…

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Q: Evaluate S ( + - + e²+ =) dz 3 · 3z 21² In x++²x+}x+ + C Option 1 √√(x³)x= √√√x + √2x+C I- Option 2

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Q: Solve. 1. Find the equation of the family of curves whose slope at any point (x, y) is 3x. 2.…

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Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: 4x Compute the values of dy and Ay for the function y = e + 3x given x = 0 and Ax = dx = 0.02. Round…

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Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: Determine the x - y coordinates of the points where the parametric equation x = 5 sin²t y = 2 cost 0…

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Q: Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 5π/4…

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Q: The area bounded by the parabola x²- 2x+y=3, the y axis and the line y=4 revolves about line y=4.…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Given

Q: Find the volume of the solid that lies under the paraboloid z = 7² - x² - y² and above region R =…

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Q: Find the general and Singular Solution of the Following differential equation y²Lny = xyP+ P²

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Q: Evaluate csc(π/6)   Enter the exact answer.

A: Solution ) csc(π/6)  Angle in first quadrant  We know that  Sin x = 1/ csc x  x = π/6 Sin (π/6)  =…

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Q: Sketch the region on the plane defined by the following integral. Then, switch the order of…

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Q: (-2,5,7) + t(-3, 1,-4) and that the point Given a line defined by the equation T = P(x, y, 15) lies…

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Q: (1,0), and (1,5). 5) Find the potential function of F(x, y, z) = (e² + ye*, e* + ze³,e³ + xe² ).

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Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4.

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Q: Answer it correctly, neatly, and comprehensively.  Written answer only.  A rectangular box with…

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Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

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Q: The following statements are true about "Integration" except: the method of adding or summing up the…

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Q: Evaluate using integration by parts or other techniques of integration. 2 9x √x² e ³x dx fx² e ³x dx…

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Q: 7. What is the LCM of 16, 24, and 40? O15360 8 O 960 O240

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the general and Singular Solution o the Following differential equation yLny = xyP+ P²

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Q: Given the triangle to 4 decimal places. x = 23 x 33° 30° find the length of side x using the Law of…

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Q: What is the general solution of the following ODE * (x² + xy − y²)dx + (²x² − 2xy) dy = 0 1 1 x³ +…

A: We know that the equation is of the form of  Mdx+ Ndy = 0  We will check whether the equation is…

Q: Find the area of the region enclosed by the given curves. y = 2√√√√x, y = x - 3,x=0, x=4

A: Given y=2x, y=x-3 x=0, x=4To find area of region enclosed between two curves:

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and…

A: To find which thing is true about given line integral.

Q: Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x2 + 16y2…

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Q: Let p(t) represent the population of a major city t years after 1950, as shown in the table and…

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