We know that if a curve C is closed, then its line integral is 0. However, in Green's theorem, it states that it is applicable to any closed curve. Please explain why they're different. Thanks!

Q: There are two tangent lines to the curve y %3D x+ 1 that are parallel to the line x - 2y = 2. Find…

A: We first find dy/dx suing quotient rule

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: ge shown below represent a curve (in black color) of quarter arde, knowing that this curve starts…

A: Given that, PU=2u3-3u2+1  -2u3+3u2  u2-2u2+u  v2-u2p0p1*** By observing the p(u) and the figure…

Q: What are Bézier curves?

A: A curve is an infinitely large set of points. Each point has two neighbors except endpoints.

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

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: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

A:

Q: Find the family of curves orthoganal to

A: Please see the explanation below

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: Find area enclosed by f(x) = x + 128 and g(x) = 160 – x4. Answer:

A:

Q: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

A:

Q: Find the lenegth of the cunde 312 2 from x=o to -

A:

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

A:

Q: A Show that the curve F(t) = lies in a plane.

A:

Q: Find all smooth curves that intersect the curves x² = y +Cx at the right angle.

A: