3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then along the upper half of x² + y = 4 from (2,0) to (-2,0)

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

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Q: A Bezier curve is defined with 4 control points as bo {0,0}, b = {1,0}, b2 = {2,-2} and bz =…

A: Beizer curve 4 control points as b0=0, 0, b1=1, 0,b2=2, -2, b3 =-2, -2 convert this in the form of…

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: 23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з…

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Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: Use chain rule to find az at (u, v) = (1, 1) if

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Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

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Q: 22 Prove that the line Z=2+46 is perpendicular to thme plane X-2y+2=6

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: 3.2 Evaluate where z = x + iy with y the path on line from z = 2+i to z = 1 + 2i.

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Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

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Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: Let F = (z, 2x, y) and C is the straight segment from (0,0,0) to (1,2,3). Then ,F dř = %3D %3D

A: Given,                                   F→(x, y, z)=z, 2x, yand C is the straight segment from (0,…

Q: 4: verify that wy = Wyx . ریاضيات المرحلة الثانية a w = In (2r + 3y) %3D

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Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: If y = xsinx then prove that y''+y=2cosx

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Q: 6) MLATU = 45°, mZSTU = 120x – 1, and mZSTA = 73x + 1. Find x. %3D %3D T. U A

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Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

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Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: 12) Show that D- d-del is shortest distance betueen a x- by +c2.of ; and ax+by tcz= dz?

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

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Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

Q: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: graph the points z = x + iy that satisfy the givenconditions. | z |&gt; 2

A: Complex numbers

Q: Show that there are point(s) (x, y, z) satisfying 2x − 3y + z − 5 = 0and lying on the line v = (5,…

A: The given equation of the line is

Q: /show that fo-1x is-Contindals everywhere.

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Q: In Exs. 19-24, find the points of in tersection and trace the curves. 19. z 3y, 3z +- y-24y +36 = 0.…

A: we have given two equations of circle and ellipsex2+y2-4ax =0…

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

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Q: 2) Evaluate yzdx+ xzdy + xydz where c is the line segment from (1,1,1) to (3,2, 0).

A: Given: c is a line segment joining 1, 1, 1 and 3, 2, 0. To evaluate: ∫cyzdx+xzdy+xydz

Q: (1) What is the relationshi etween lines 11 and 12? wl Y = 2 y = 1+ 2t Z = 1+t

A: Given: L1:x=2        y=1+2t     z=1+tL2:x=4-t   y=1+t      z=2+t

Q: Compute / (1/zy, 1/(z + y)) dr along the path from (1, 1) to (3, 1) to (3, 6) using straight line…

A: The parametric vector form of a straight line from (1,1) to (3,1) will be given by:…