Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a line from point (-1, -1) to point (1, -1), C2 which is a line from point (1, -1) to point (1,2), C3 which is a line from point (1,2) to point (-1, 4) and C4 which is a line from point (-1, 4) to point (-1, -1) as shown in the following figure: (-1,4), (1,2) (-1,–1) (1,–1)

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: Evaluate A = F. dr where F(x, y) = (6x – 2y)i+x²j for each of the following curves. a) C is the line…

A:

Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

A:

Q: 5) Find the distance between the pole and the point (r, 0) = (-1, ). %3D

A: A detailed solution is given below.

Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: If y=f(x) be the curve that lies on the xy plane, then its length from x=a to x=b is given by…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.