Evaluate | (transparent gamma symbol) ∫(x2 + y2) dz | where z = x + iy with (transparent gamma symbol) the path on line from z = 2 + i to z = 1 + 2i.

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

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Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: The curve y et and the lines y = 0, x = 0, and x = In 2 %3D

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: C is polygonal path from (0, 0) to (3,0) to (3, 2); the sur- face is f(x, y) = 2x +y

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Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

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

A: In the question it is asked to find the path of a heat-seeking particle placed at point P. Given:…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: The length of the curve y = from x = 0 to x 6 is

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: (A) Evaluate" [(x² + y)dx + (x+1+d along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost…

A: What is Line Integral: When we integrate a function along a straight line or a curve inspite of…

Q: Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of…

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Q: Part (a) Evaluate 4e*dz, where C is the polygonal path consisting of the line segments from z = 0 to…

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Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: 7. Find the length of the curve y = x/4 on the interval [0,8] %3D

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Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

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Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: Use the Path Length formula to find the path length of the function over the given interval. Path…

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

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Q: Rule: (x, y) → ( Reflection: Across Line y = x

A: Actually the rule of reflection along y=x is simply writing the points (x,y) as (y,x). See for the…

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

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Q: Find a curve through the point (1, 9 whose length on the interval [1, 2] is given by i VI+ 25z!0dz-…

A: Explanation: Given a curve, ∫121+25x10dx Function f(x) has an arc length on the interval [a,b] is…

Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

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Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…