s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0) to (3, 1).

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

A:

Q: - Compute 5y dr a dy, where C is the arc of the parabola y = from (-2, 4) to (0, 0).

A: The line integral of the function with respect to x, y is solved using the formula…

Q: 2.2 Prove that Te -dz < 3 ez z2 +7+1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

A:

Q: Find the arc length of the curve C from the origin to the point (1/2, 1/6, 1) , where C' is the…

A: Given equations are z2=2x and 3y=xz. Now multiplying z2=2x with z:  z3=2xzz3=6y

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

A:

Q: 32. At what points does the helix r(t) = (sin t, cos t, t) intersect the sphere x? + y² + z² = 5?

A:

Q: Compute the arc length of the parametric curve given X=1/3t^3-t,y=t^2+3 From t=0 to t=3

A:

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

A:

Q: Use Green's theorem to evaluate 2y3 dx – x³y2 dy, where C is the positively oriented circle of…

A:

Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

A:

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

A:

Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference…

A:

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A:

Q: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

A:

Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

A:

Q: The curve y V4 – x², – 1 < x < 1, is an arc of the circle x² + y? = 4Find the area of the = 1…

A:

Q: Compute the arc length of the indicated portion of the curve: 7(1) = (7 +2r²)î + (21² – 4)ĵ + (7 –…

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

A:

Q: Use Green's Theorem to evaluate dr, where F-(VE+ 4y, 2+ C consists of the arc of the curve y 1z - z…

A:

Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

A:

Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

A:

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: Compute ž dz +y1 z dz, +72 and where +Y1 is the segment from 1 to -1, and +y2 is the arc on the unit…

A:

Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

A:

Q: Jse Green's theorem to evaluate $ (2°e* + 4y) dz + (-5x+ y* sin(y)) dy, where C is the…

A: The given path C is circle x2+y2=16. Therefore: D= (x, y) : x2+y2≤16

Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: From Rogawski ET 2e section 8.1, exercise 11. Approximate the arc length of the curve y = i x4 over…

A:

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Prove that e dz < ++1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: 4. Let C be the positively oriented circle centered at the origin with radius r> 3. Without…

A: Given: Let C be a positive oriented circle centered at the origin with radius r&gt;3. Without…

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

A:

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

A:

Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: Are there any points on the hyperboloid r² – y² – 2² =1 where the tangent plane is parallel to the…

A:

Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

A:

Q: Use Green's Theorem to evaluate F. dr, C where F = (Va + 6y, 4x + /ỹ C consists of the arc of the…

A: