Write a parametrization for the straight line path from the point (3,3, 4) to the point (5, 2,-4). x(t) = %3D y(t) = z(t) %3D where 0

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: Find a parametrization for the cylinder x2 + y2 = 1.

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Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Let C be the parabola y = x² for 0 < x < 2. Let F(x, y) = ye"i + xe*"j.Compute the line integral

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: 2. || F. dš where F = 3x i+ 2z3+ (1- y²) k and S is the portion of z = 2 – 3y + x? Evaluate %3D that…

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Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: Evaluate the line integral/ (ax + 2y)dx +x dy, where C consists of the path C from (0,0) to (3,0),…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Find a parametrization a = #(t), y = y(t), t E [0, 1] for the line segment from (-2, –5) to (-3,…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Consider uxx + auxy – 2uyy + ux + 2uy = 0 Find all values of a so that the PDE is Hyperbolic.

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Q: Find a parametrization of the paraboloid given by f (x, y) = x 2 + y2.

A: To find a parameterization of the paraboloid given by: fx,y=x2+y2

Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

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Q: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line…

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Q: 2 The values of a and b such that the surfaces ax - byz = (a + 2)x and 4x2y + z3 = 4 cut…

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Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y² = 1}, that…

A: The parameterization of a circle  that generates the clockwise orientation of C is given by: x=r…

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: Which of the following is a parametrization of the line through P = (3, 10, 8) perpendicular to the…

A: Use Parametrization to solve

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0&lt;= x &lt;= 2, 0…

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Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: Evaluate R CF. dr with F(x, y, z)=(x2 + y)i – (3xz)j + (z – 4y) k, with the path C as the line…

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Q: Find a parametrization for the line segment from 2₁ =1-i to Z₂ = 2i. A. 2 (t) = 1 -i + (−1+3i) t 0…

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Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

A: Value of the given integral is

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y+ 12z on the elipse…

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Q: Find the flux of F = z²k upward through the part of the sphere x² + y² + z² = a² in the first octant…

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Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

Q: Let C be the boundary curve counterclockwise of the semidisk æ? + y? 0. Then fc(-2ydx + 3xdy) 5dydx…

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Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: What is the correct piecewise parametrization of a path C created by starting from C₁ of equation y…

A: Concept: We have given the curves  y=x+3x=0 to x=4y=x2 Here the red line represents y=x+3 The green…

Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

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Q: OFind the orthogonal Tradectories of the families of y2-5ax 42 - %3D where a being a Parameto

A: For find the orthogonal trajectory replacement of dy/dx with (-dx/dy) is required.