dy for the curve defined by x° – y = 2xy? dx Which of the following is O 2x + 3y? 3x2 – 2y O 3x2 – 2y 2а + 3у? O 2x² – 3y - 2x + 3y2 O 3x² + 2y 2л - Зу? | O 3x² – 2y 3x + 2y?

Q: Let C be the curve y = x³ – 3x2 + 4x - 1 joining the points (1, 1) and (2, 3). Find the value of |…

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Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

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.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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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: nd [(dy)/(dx)] if the curve is defined by 7 x? e7y + 6 y² e² x

A: We are asked to find the derivative

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

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Q: Evaluate S. x?dz + z?dy + y?dx where C is the curve x = t2 ,y = t², z = t² from t = 0 to t = 2.

A: We will use concept of line integral to solve this.

Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: b. The curve y = cosx ,y 0, x = - and x=

A: Solution Question 26 b Given, The curve y = cosx  We have to find the area of region bounded by the…

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: 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: Compute f ds for the curve specified. f(x, y, z) = 2x2 + 8z, c(t) = (e*, t², t), 0 sts 1

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Q: Cvaluate (xy) s ds where C is the curve y = x², for 0 < x < 2.

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Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 <ts 2

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Q: II. Find the acute angle between the given curves. 1. y'=2x^4x+4y'+5 y=0 2. x'y+4a y=8a°nx²=4 ay 3.…

A: As per bartleby guidelines we only give first question answers.

Q: The value of le ydx + zdy + xdz where C is the curve x = y = z = 2t2 from t = 0 to t = 1 is A В 15 C…

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Q: At the given point, find the line that is normal to the curve. 2x y-cos y 3x, (1,x) 1 O A. y= -7**7…

A: The given curve is 2x2y – π cosy = 3π and the point is (1, π). Evaluate the slope of the tangent to…

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: Find a rectangular-coordinate equation for the curve x = 2cos(t) and y = 3sin(t), 0 <t < 2n.

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Q: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

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

A: 9

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

A: iGivenx=t−3    .........1y=3t−7  .........20≤t≤3Now elliminate "t" from equation 1 and 2 by…

Q: Let æ = 3t, y = - 7t3 + 63t2. dy as a function of t, then find the slope of the parametric curve at…

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Q: Find the points on the curve c where the tangent is horizontal C: x= t? + 2t, y = t - 48. ОА (-128,…

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Q: Let x = 11t², y = 9t6 - 2t². d²y Determine as a function of t, then find the concavity to the…

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Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: b. The y' of the curve y 4 Vx

A: The given function is y=4x. Obtain the first derivative as follows. y'=ddx4x=ddx4 x-12=4…

Q: Consider the curve x²y + y2x = 6 %3D Find the coordinates of the point (x,y) where the curve has a…

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Q: For the curve y= e^-3x cos 2x, determine y'' + 6y' when x = 0.

A: In this question we will use basic of calculus concept of differentiation. We will simply…

Q: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

Q: dy of the curve yln x + 5x² + y' = 13 at the point (1,2) dx b) Find

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Q: Sketch the curve x = 3sin2t, y = 4cos2t

A: This question is taken from the function in which we have to sketch the given function parametric…

Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 sts 2

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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: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: Consider the curve x²y + y²x = 6 A) Find in terms of x and y dx

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Q: Find the length of the curve y- v2- 2,0 <z<1 O a. b. V dz O. So Vi 2-2z od. fo dz 2+2 2-2z

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

Q: Q22. determine the family of curves that is orthogonal to the family Zy²+3x²=X when z > O and yea.…

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Q: Consider the curve given by y2+xy=x3-(2y/3)+(3x2/4) a) Find all the points (x,y) on this curve…

A: Given is the equation  y2+xy=x3-2y3+3x24..............................(1) The objective is to find…

Q: Find [(dy)/(dx)] if the curve is defined by 7 x² e7 Y + 6 y2 e2 x = 16. %3D [(dy)/(dx)]

A: Given:     7x2 e7y + 6y2e2x = 16

Q: y(z) along the curve given by r" = e*.

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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: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

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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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