Siceteh the curve in the compeex plane 1. 12-31= 12+3i/

Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: Find parametric equations for the line through (7,4, – 7) perpendicular to the plane 4x + 5y + 4z =…

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Q: Discuss Green’s Theorem in the Plane?

A: Green’s Theorem : Green’s theorem is one of the four fundamental theorems of calculus, in which all…

Q: Find parametric equations for the lines with the given description.Perpendicular to the xy-plane,…

A: The line is perpendicular to the xy-plane and passes through the origin;

Q: Find a parametrization for the curve described below. the line segment with endpoints (1, – 4) and…

A: Given:   Endpoint : ( 1 , -4) and ( -2 , -7)

Q: Find the distance from the point Q to the plane p. Q= (2, 2, 2), P with equation x + y - z = 0

A: Given equation of plane is x+y-z=0 and given point is Q(2, 2, 2).

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: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Find equations of the Normal plane and Osculating plane of y = 2t , the curve x = 2 sin 3t , z =…

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Q: Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2).…

A: Here we have to find the parametric equation of the line that passes through the point P(4,2,-3) and…

Q: distance

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Q: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t , y = 2t, z =…

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

Q: Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane  c.xz-plane.

A: a) Distance of (3, -4, 2) from xy plane:On xy plane , z=0. So, This point is 2 units away from the…

Q: Find an equation of the plane. The plane through the point (5, –1, –6) and parallel to the plane 5x…

A: Given point is (5,-1,-6) and plane is 5x-y-z=3 find the equation of the plane which is parallel to…

Q: Find the distance from the point (−5,2,−3) to the (a) xy-plane (b) xz-plane (c) yz-plane (d) x-axis…

A: We know that distanced of xy-plane from the pointx0,y0,z0 is given by d=z0…

Q: गाण the Simultaneous earvation. ntuy-4 the linel in ay Plane and indiceate the solu tion.

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Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find parametric equations of the normal line to x² the surface z = + y? 4 at the point (2, -3, 10)

A: Given curve

Q: Q5] What is a parametric representation of a curve? What is its advantage?

A: We are entitled to solve only one question at a time so we will answer only the first question.…

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Find the distance from the point (2, 1,−2) to the plane 6(x − 1) + 2(y − 3) + 3(z + 4) = 0

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Q: The Cornu spiral is the plane curve r(t) = (x(t), y(t)), where u2 u? x(1) = sin du, y(1) = cos du 2…

A: Solution:- Cornu spiral is the plane curve r(t)={x(t), y(t)} ⇒xt=∫ot sinu22du dxdt=sin…

Q: Dar Show that the length of the the Curve y=foor where Fox)= Insee t

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Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

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Q: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

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

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: 3. Find an equation the plane curve about the inc

A: INTRODUCTION: In mathematics, functions are the most fundamental aspect of calculus. Functions are…

Q: dz -, n = 2,3, 4, ... where z = a is inside the simple closed curve C. (z – a)" Evaluate

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Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

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Q: Va+ ド+で Find the distance between the point (0, 1,5) and the plane 3r + by – 2z-5 0.

A: topic - distance of point from plane

Q: Find parametric equations for the line through the point  (0, 2, 2)  that is perpendicular to the…

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Q: Find the linear speed v for a point on the edge of a flywheel of radius 2 m, rotating 42 times per…

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Q: Find the distance between the point (3, −2, 4) and the plane 2x − 5y + z = 10.

A: Given: The equation of a plane is 2x-5y+z=10. To determine: The distance between the point 3,-2,4…

Q: Find a parameterization for a circle of radius 4 with center (-3,-1,2) in a plane parallel to the xz…

A: Aim: To find the parametric equation for the circle of radius with radius 4 and center -3, -1, 2…

Q: Find equations of the Normal plane and Osculating plane of the y = 2t , curve x = 2 sin 3t , z =…

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Q: Show that the curve al lies in plane and b) finel the equation of the plane that contains the curve…

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Q: Find the point(s) of intersection of the curves r = 1 and r = 2 sin 0. ^(1.5)(1.플) 1, 27 3 В. 1, 1,…

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Q: Find equations of the normal plane and osculating plane of the curve at the given point. x = sin 2t,…

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Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: Find the diffetential equation of the family of plane curves described, Draw at least three members…

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Q: Q = (-1,3,–1) on the plane Find the point P nearest to x – 4z = 2

A: Given, Q=(-1,3,-1) x-4z=2 (equation of plane) x-4z-2=0

Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.