|Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is formed by y = 5x, y = 14 – 2x and x = 7 for which x, y > 0.

Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

A:

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

A:

Q: The equation of tangent plane to the surface f(x, y, z) = x² + y? +z-9 = 0 at the point (1,2, 4) is…

A:

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

A:

Q: c) By using Green's theorem evaluate $ (4.cy – y*) dx + (2³ + 3xy) dy where C is a closed curve…

A:

Q: *Gl0/ Apply Stoke's theorem to Cal cu late S4y dx +2zdy + 6y dz where c i$ the curve of xyt 2 = 6z…

A: Apply Stokes theorem to calculate ∫C(4ydx+2xdy+6ydz) where c: intersection of x2+y2+z2=6z and z=x+3…

Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: Find an equation of the tangent plane to the surface g(x, y)=x²-y² at the point (7, 4, 33). O…

A:

Q: 1. Use the tangent plane to the surface f(x, y) = x² + y? mate f(1, 2). at the point P(-1,1,2) to…

A:

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

A:

Q: Evaluate f. x'dz +z?dy +y?dx where C is the curve x = t ,y = t2, z = t? from t = 0 to t = 2.

A:

Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

Q: Evaluate S. x?dz + z?dy + y?dx where C is the curve x = t2 ,y = t², z = t² from t = 0 to t = 2.

A: We will use concept of line integral to solve this.

Q: 14. Evaluate | (zx² + y°) ds where C is the curve of intersection between the cylinder x? +y² = 4…

A:

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

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: Verify Stokes’s theorem for F = , where C is the curve C: x2+ y2=4 , z = 2.

A: Stoke's theorem problem...

Q: Find the length of the curve y =/2 from z = 0 to z = 3. %3D

A: Integration of (1+(f'(x))2)1/2 form 0 to.3

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

A:

Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

A:

Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, x + 3z, 2x + 3y). (b) If C is the curve…

A: Let the function f(x, y, z) = xy + 2xz + 3yz which satisfies the given property  Gradient (f) = ( y…

Q: 3. Below is a curve C, which is the intersection between the surfaces S1: z = 4 -x? and S2: z + 2x…

A: A is the correct answer.

Q: The plane y = 1 intersects the surface z = x^4 + 6xy − y^4 in a certain curve. Find the slope of the…

A: The intersection of surface z=x4+6xy-y4 and plane is y=1 is z=x4+6x1-14z=x4+6x-1

Q: The curve r+y-6x2y 0 is symmetric about Oy = 0 Ox = 0 Oy =x None of these

A: We need to check the symmetry of the curve x4+y3-6x2y=0

Q: 6. Let a curve be parameterized by x = t³ – 9t, y = t+ 3 for 1 < t< 2. Find the ry coordinates of…

A: Given that

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

A:

Q: Find the work done by F = xyi+yj - yzk over the curve r(t) = ti + t²j + tk, 0≤t≤1

A:

Q: The equation of the tangent plane to the surface X +y- z = (2, –1, -1) is 2 at the point | O a) None…

A: This question can be solved by applying the formula of equation of tangent plane to the given…

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

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

A:

Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

A:

Q: F(x, y) = 2xyi + (y² – x²)j (x2 + y2)2 and C is any positively oriented simple closed curve that…

A: Given  F(x,y) = 2xyx2+y22i+y2-x2x2+y22j To Evaluate  ∫CF(x,y)dr

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

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: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

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

A: Green's theorem in a plane: If D is a region inclosed by a closed curve C then ∮C u dx+v dy=∫∫D…

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

A:

Q: Find the Length L of the curve R(t)= -2cos(4t)i + 2sin(4t) j + t k over the interval [2,6]. L =

A:

Q: Find the length of the curve r(t) = (√2t)i + (√2t)j + (1 - t2)k from (0, 0, 1) to (√2, √2, 0)

A: given, r(t)=(2t)i +2tj+1-t2kwe have to find the length of the  given curve from (0,0,1) to 2,2,0

Q: Let C be any curve.

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: The posted question has multiple questions but according to guidelines we will solve the first…

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: determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.

A: Curve will have critical point if it have vertical tangent or horizontal tangent . Slope of…

Q: Determine the equation of the tangent plane to the surface z=x - 3xy + y at the point P (2, 1, 3).…

A: Solution

Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

A:

Q: Find the family of curves orthogonal to the family 4y2 + 3x2 = k when x > 0 and y > 0. (A) 3y2 – 4x2…

A:

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

A:

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

A: knlk

Q: Q 3. For a curve in the x y plane differentiate between dy and dy. Brief and to the point answer is…

A: Query- For a curve in the x y plane differentiate between dy and δy, write the answer briefly,…

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

A: