Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is formed by y = x, x² + y² = 4 and y-axis for which х, у 2 0.

Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Let l be the line given parametrically by x = (1, 3) + t(-2, 1), tЄR. Which of the following points…

A: A parametric equation is an equation that employs an independent variable  to define the dependent…

Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

A:

Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: 3. Show the parametric form of the line that passes through points A(3, 6, 1) and B(2,10, 5) Compute…

A:

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: 3. Find the 1-parametric equation of the line in the plane passing through the vector P=[]-[9] Hint:…

A: p = [-3,2]q = [0,-3]now find parametric equation lines