IV Evaluate f F. dR given that AF (1, y) = 2y i+ (ry – 2r)j and C is the curve in the third quadrant from the point (0, -2) to (-3, 0) along the ellipse 4x2 + 9y? = 36. %3D

Q: c) By using Green's theorem evaluate $ (4.cy – y*) dx + (2³ + 3xy) dy where C is a closed curve…

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Q: 口 38 Which one of the following equations describes the tangent plane to the curve, f(x, y) =…

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Q: 2. Let F = (-y/2, x/2), and let C be the curve shown below. What is F ds? Explain %3D why. y 1 1 2 3

A: The vector field is F=-y2, x2 C1:0, 0→2, 0rt=2t, 0, r't=2, 0 F=0, t Hence, the integral becomes…

Q: Find the length of the curve C defined parametrically by C: 2(t) = e'cost, v(t) = e'sint, 0SISR…

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Q: d'y at the point dx2 (c) Evaluate on the curve where x = -1 and y = 1. %3D %3D

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Q: Q3/ Find the acute angle between the two curves at their points of intersection: r = 2si n 0, r =…

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Q: 14. Evaluate | (zx² + y°) ds where C is the curve of intersection between the cylinder x? +y² = 4…

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Q: H. Grven F(xy,2) = 9x²+y² +%Ž-37 . Frind the equation of the tangent plane and ormal line to the…

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Q: (b) The curve y = x +3x, from x 1 to x = 3 (c) The ,2 1 from 2 to g

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Q: d²y Find- when t = 1 if given the parametric functions as below, dx2 x = 3e5t y = te-5t

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Q: dy/dx The DE yet describes the slope of some curve y=f (x) in the xy-plane at every point (x,y)…

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Q: de termine d3y f the parametric equatio ns. of dx2 x (t) = tlht and ylt) = (t-1)-

A: This question is based on diffrentiation of parametric curves.

Q: Evaluate given that F (7, y) = 2yî + (zy – 2r)j and Cis the curve in the third quadrant from the…

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Q: Evaluate fF dR given that F(x, y) = 2yî + (xy – 2x)j and C is the curve in the third quadrant from…

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Q: Find the equation of the tangent plane to the surface z = 9y? – 4x² at the point (-3, –3, 45). e:…

A: Given query is to find equation of the tangent plane.

Q: Q5. The curve y = ax? + bx + c passes through the point (1, 2) and is tangent to the line y =x at…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Let f (z)=7. Find f (z )dz from z =0 to z =4+2i along the curve C given by z =t? +it. (A) –10 – (C)…

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Q: a)Find the exact length L of the curve 3y? = (4x – 3)°, 1 0. Answer: b) Evaluate Sxe*dx Answer: 1 c)…

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Q: late the F= (x - y) i - (x 2 + y 2) j; C is curve from (4, 0) to (-4, 0) on the upper half of the…

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Q: Let the equation of curve c be x=2t, y=t3, t∈[0,2]. What is the value of the integral ∫c -y2dx +…

A: Explanation of the answer is as follows

Q: Find F-dX where C is the curve X(r) = r°I+( 2r+ 1J, 0<I55, and Fxy) = rI+yJ.

A: 9

Q: Q2: (a) Sketch the domain of f(x, y) = Vx + Vỹ on the ay-plane (b) Sketch the level curve of g(x, y)…

A: (a) To sketch the domain of f(x,y)=x+y The above function is defined only if x and y are…

Q: x2 + 4 Find the equation of the tangent plane to the surface z= 2 at (4,3,-3) | 9

A: The equation of the tangent plane to the surface at (4,3,-3) is, 6x + 2y + 3z = 7  The detailed…

Q: The curve r+y-6x2y 0 is symmetric about Oy = 0 Ox = 0 Oy =x None of these

A: We need to check the symmetry of the curve x4+y3-6x2y=0

Q: Find for the parametric curve c(t) = (41°, 2r² – 8) at the point t = 2. (Use symbolic notation and…

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Q: The plane x = 1 intersects the paraboloid z = x2 + y2 in a parabola. Find the slope of the tangent…

A: Given that the plane x = 1 intersects the parabolic z = x^2 + y^2 in a parabola.   So,…

Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

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Q: The tangent line to a point on the curve r(t) = (3t2 + 2t+ 3)i + (t² + 2t + 4)j+ (2t2 +t+ 2)k…

A: Differentiate:

Q: The tangent line to a point on the curve r(t) = (3t² + 2t + 3)i + (t² + 2t + 4)j+(2t² +t+ 2)k…

A: Differentiate:

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: 3. Find a parameterization of the curve C= r(t) = (x(t), y(t)) a. Where C is the line segment…

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Q: The value of [F. dī where F= x?y² i + y j and C is the curve y? = 4x in the XY-plane from (0, 0) to…

A: I am solving this in step 2.

Q: 2 Ex3/2 between x = 0 and x = 1 is 3 %3D %3D The length of the curve y

A: Introduction :

Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

Q: 4 Find the length of the curve y=x3 3 %3D x3 +5, 1 Record Audio Record Video Add a File

A: To find out the length of the curve.

Q: 4x2-4xy+y2-6x+8y+13=0 find this curve's  central  coordinates

A: Given,    4x2-4xy+y2-6x+8y+13=0   It is a equation of parabola.

Q: Evaluate F•JR given that F (7, y) = 2yî + (zy – 2x)ĵ and Cis the curve in the third quadrant from…

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Q: dy in terms of t: Differentiate parametrically to find dx x = 4t2,y = 2t3 None of the other answers

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Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

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Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

A: Since you have posted multiple questions, we solve the first part of the question, To get the…

Q: Consider the curve r (t) = (t, t°, tº); t > 0 Find an equation for the projection of the curve on…

A: We have to find the projection in xz plane so simply find the relation between x and z

Q: y2 Find the length of the curve x = + from y = 1 to y = 2. %3D 8 1

A: We will calculate the length of the asked arc as-

Q: Find fF - dř where F(x,y,z) = (3ye", 6ye - 1+) and Cis the curve = (sin t,2- for 0 SISE. F(t)

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Q: Q5)The distance from the point p (2,-3,4) to plane x+2y+2z=13 is 3 * .units F T

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: J1 (x²+8)3/20 Find the length of the curve x = y²-n, 1≤ y ≤e². The given curve is rotated 8

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Q: y = V36 – x² What is the length of the -3<x<3 segment of the curve 20 - y = V36 – x² eğr OA) 2*pi В)…

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Q: c) By using Green's theorem evaluate $ (4xy – y°) dx + (x³ + 3xy) dy where C is a closed curve…

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Q: Use implicit differentiation to find all points on the graph of y* + y² = r(x – 4) at which the…

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