Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter clockwise sense.

Q: 2. For the equation 2x² + 2xy + 2y²-2x-10y+11= 0, eliminate the xy term by rotating the coordinate…

A: Given: The given equation of the conic is 2x2+2xy+2y2-2x-10y+11=0.                      ...........1…

Q: Find the equation of a circle centered at (1, −1) and tangent to the line 2x + 3y = 12

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Q: 2. Find the coordinate of A(-4,6) after it has been rotated 90 degrees counterclockwise, reflected…

A: When we rotate by 90° counter clockwise, the x coordinate become y coordinate of the point after…

Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: what would be the inebriation of the figure below after a reflection across the x-axis?

A: We have to find the reflection of the given figure accross x axis.

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

A: Given that the osculating circle  y = x

Q: Let C' be the circle |2| = 3 in positive sense. Find ( sin(r2*) + cos(72²) dz cos(T2²) (2 – 1)(2 +…

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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: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

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Q: Use the substitution u = x² and the equation of a semicircle to evaluate 4XV4 - x* dx.

A: Given the integral  I =∫024x 4-x4dx To evaluate the integral :- Using the substitution,  u = x2  du…

Q: Evaluate fory³ dx-4x dy, where C is the portion of the circle centered at the origin of radius 1 in…

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Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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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: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)

Q: Find the acute angle between 3x – 2y + 7 = 0 and 2y + 4x – 3 = 0 (to nearest degree).

A: Given, 3x-2y+7=0      .....12y+4x-3=0      .....2