c) By using Green's theorem evaluate OUIM GUTM U where C is a closed curve starting from the origin to point (0, 1) along I. (try – y°) da + (x* + 3ry) dy the y-axis, then to point ( ) along the semi-circle

Q: Find the curvature k of the curve C : 16 =1 at the point (0, 3)

A: 1. convert the equation into parametric form 2. use formula for curvature written below

Q: By using Green's theorem evaluate £ (Ary – y") dr + (** + 3ry) dy where C is a closed curve starting…

A:

Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

A:

Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

A:

Q: Or Using Green's theorem find the value of 6 F. dr Where F(x, y) = (2e-5x – y²)i + (y³ + 2x²)j and C…

A:

Q: 4) a) y»*>O impenting y= # Curve, x =0 and y Colculote the orea af the regien betueen the lines by…

A: Solution to section (b) as requested:

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

A: Find your answer below

Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

A:

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

Q: c) By using Green's theorem evaluate $ (Ary – y*) de + (* + 3ry) dy where C is a closed curve…

A:

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: b) Calculate again an approximate value of the length L of the curve arc from the previous…

A: The distance (d) between two points (x1,y1) and (x2,y2) is given by the equation;…

Q: The value of le ydx + zdy + xdz where C is the curve x = y = z = 2t2 from t = 0 to t = 1 is A В 15 C…

A:

Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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: Find F. dr where C is a circle of radius 2 in the plane. x+y+z 9, centered at (4, 3, 2) and oriented…

A: Consider the given equation: And the plane x+y+z=9 centered at 4,3,2.

Q: 13. Let C be the unit circle |z| = 1, described in the positive sense. Determine the %3D value of c…

A:

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

A:

Q: Use Green's theorem to evaluate ſ. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: We have to evaluate the integral ∫5xy+x2+y2dx+x2-ydy over the closed curve C. Comparing with…

Q: c) By using Green's theorem evaluate UTM £ (kry – y") dz + (z² +3ry) dy where C is a closed curve…

A:

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

A:

Q: Show that the curve given by, R(t)=(2sint)i+(2sint)j+(sqrt(8)cost)k lies on a sphere centered at the…

A: The equation of a sphere, centered at h,k,l, is defined by the equation, x-h2+y-k2+z-l2=r2 , where,…

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

A:

Q: Find the length of the curve r(t)=, -2 "< or equal to" 0, "< or equal to" 2.

A:

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

A:

Q: Find the curvature k of the circle C : (x – 2)² + (y+ 3)² 16 at the point (2, 1).

A: Use the formula of curvature to solve this problem.

Q: 2. A CIRCLE IS TANGENT TO THE CINCLES x7 y? = 4 x*+ y? = 12Y+ 64 2 F IND THE LOcuS OF IT3 CENTEN AND…

A:

Q: (a) Prove that curves a, ß: I → R² are congruent if k̟ = Kg and they have the same speed.

A: Part (a):   If any two continuous function defined on the interval I, and the two curves are…

Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

A:

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

A:

Q: )مه و و ي (x2 + y?, y* + 4x) · dr (2,1) )هد0( )ه,(

A:

Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

A:

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

A:

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

A:

Q: The curve C is the circle of radius 19 contained in the plane z = 19 and centered around the z-axis,…

A: …

Q: ind the the exact length x = et – t, y = 4e/2, |

A:

Q: Find the curvature k of the curve C: 16 + =1 at the point (0, 3)

A: To find the curvature of the curve at the point (0,3).

Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

Q: Let C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. Evaluate (sec…

A:

Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

A:

Q: Find the DE of the family of plane curves describe and sketch some of its members. Straight lines…

A:

Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

A:

Q: c) By using Green's theorem evaluate $ (4xy – y°) dx + (x³ + 3xy) dy where C is a closed curve…

A: