4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going in counterclockwise direction.

Q: 3.Find [, (3x² + y)dydx -2

A:

Q: C is tG line Geament faom (i,3) to (5,-8) fompute f (x -y) dv Rdp

A:

Q: if y = 3x² – 4r³ + 3ª + VI + a, then dy/dr is:

A: Given that     y = 3x2-4x5+3x+√x+π Here we have to find dy/dx . We know that        dxn/dx = nxn-1…

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

A:

Q: Calculate (x+y+z) ds

A: In this question, we evaluate the surface integral for the given intersection of the curves.

Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

A:

Q: Standardize the cone with equation 7x2+4xy+4y2-8x-12y+9=0

A:

Q: 323 + 4z2-5z+1 dz (z-2i)(23-2) 1. Compute: where C = {|z| = 3} is the circle of radius 3 centred at…

A:

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: 2: Clasafy ad Solve The fllowing diffrential equatóns dy -2x e + + 4. Sinx フス2 フィ* + (6 y = 6x°1ox…

A: The general solution of an ordinary non homogeneous differential equation is the sum of…

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

A:

Q: Please

A:

Q: 3.Find [, L (3x² + y)dydx

A:

Q: enter-radius form of the equation of t

A:

Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

Q: Find the number of common tangents to the circles x\power{2}+y\power{2}+2x+8y-23=0 and…

A: For x2+y2+2x+8y-23=0 ,C1≡(-1,-4),r=210for x2+y2-4x-10y+9=0,C2≡(2,5),r=25now C1C2=distance between…

Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

A:

Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

A:

Q: Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown. -…

A:

Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…