8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the counterclockwise direction with vertices (0,0), (4,0), and (4,2). You may use any appropriate method.

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A: We can answer the question as below.

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A: Given:  a=9 and b=4 To find:

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A: Given that                                  F→ = ∇x2+y2  we can written this asF → =…

Q: Perform the calculation. 90° - 58°20' 32°20' 31°20' 31°40' 32°40'

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A: Given.

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A: We need to determine discontinuity.

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A: The given functions, a) f(x)=2x3-3x2-12x+1, -2,3b) gθ=θ+cotθ2, π4,7π4

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A: f(t)=(et-e-t)2

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A: This is a basic trigonometric ratios problem

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A: Given:-y=5x2+3dxdt=2 at x=3To find : dydt

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Q: 4. Evaluate the integral 1 tanz+ tana+ x 2(x² + 1) + C 2(x²+1) x da 24 +22² +1 (d) tan-¹+ +C (e)…

A: To evaluate: I=∫dx(x4+2x2+1)=∫1(x2+1)2dx

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A: We will solve the required.

Q: 11. 12. 13. 14. 15. 16. 18. 19. For items 11-25 consider g(x) as defined below. 20. I. lim g(x) does…

A: Solution is given below:

Q: What is F(x) = f +/dx? O F(x) = 4 ln x + C ○ F(x) = 4 ln x O F(x) = 4 ln |x| O F(x) = 4 ln lxl + C

A: We can find the correct answer as below.

Q: Evaluate ff sin(9x² + 4y²) da, over the region in the first quadrant by the ellipse 9x² + 4y² = 1.

A:

Q: explain

A: Displacement is the shortest distance between two point.

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A: To evaluate the binomial coefficient.

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A: Solve the following

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A: A graph of the function f is given below. To determine the correct choice for items 4, 5 and 6.A if…

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A: We have to sketch the graph and state the transformations.

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A: Topic = Algebra

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A: We need to determine discontinuity.

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A: Given data:- ∫csc22xxdx

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A: NOTE: Refresh your page if you can't see any equations. . ................upper and lower limits…

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Q: (15) Complete the table: fcf(x) dx S[f(x) + g(x)]dx f[f(x) = g(x)]dx fkdx fx" dx f sin(x) dx f…

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