1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1 centered at (0,0) oriented counterclockwise.

Q: y = ay +b cos(wt) Scale and non-dimensionalize: C1 C2 Pick c1, c2 + change variable

A: We have to define this partial derivative in terms of x and t

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A: Given data:     The given differentiable equation is: .   The expression for the linear…

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Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: Graph: y = 2 sin 27x, 0 s xs 2.

A: To graph: y=2sin2πx,     0≤x≤2 Solution: We know, for a sine curve of the form: y=asinbxAmplitude…

Q: (d) § (Vx+sinx) dx

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Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

A: To solve the line integral ∫(2x - y)dx + (x + 8y)dy over the curve C, which is the x-axis segment…

Q: Evaluate (24 + x³)dx where C is the line segment from (−2, −1) to (0, 1) followed by the right half…

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Calculate using polar coordinates: 1-x² x. y. √ x²+y² dy dx So So

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Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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Q: dy Write an equation for dx on the ellipse y = y² + x2 3, showing ALL - your work. Then find the…

A: We differentiate both sides with respect to x and then solve for dy/dx.

Q: f circle, x2 + y2 = S.

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Q: 33. Find the directrix. (y- 9)2 - 8 O y = -9 O y = -7 O x = -7 | x = -9

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Q: see thee quation as atached here

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Q: Calculate (ay² + y) dy dæ. 3.

A: We use the properties of integrals to evaluate the given integral.

Q: Evaluate o y dx – x³ dy, where C includes the two circles of radius 2 and radius 1 centered at the…

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Q: l, (2 Y - x ) dA,where R is the region of the first quadrant bounded by the circle x2 + y? = 4 and…

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Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

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Q: dy Consider the parametric equations x = e' -1 and y=1-t. Which of the following represents dx 1-12…

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Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 3

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Q: - z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

A: Given differential equation, 1-x2d2ydx2-2xdydx+30y=0 Find the largest root from the indicial…