Question 1. Use Stokes' theorem to evaluate SF · dr, where C is the circle x2 + z² = 2, y = 1, and F = (x²z + y?, e" sin(yz), 2xy – 2²x).

Q: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. circle: x = h +…

A: We know the trigonometric identities Sin2θ + cos2θ = 1

Q: Question 10. The curve r(s) = (s,3 cos , 3 sin ) is parameterized by arc length. Find the…

A: The curve, r(s)=<45s,3coss5,3sins5> The Frenet-Serret frame {T,N,B} for r(s) are given by, The…

Q: Consider the following. X = sin y = os(플e), -π sθ<π (a) Eliminate the parameter to find a Cartesian…

A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1

Q: QUESTION 17 Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). 2 How…

A: Given - Let a, b, c be the last three digits of your student ID and let d = max(a, b, c) To find -…

Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

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Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

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Q: Question 4. Calculate the arc length of the polar curve r = a(1 – cos 0).

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Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

A: I am attaching image so that you understand each and every step.

Q: 10. Identify the surface that is given by: p (sin? (6) cos (0) + cos ()) = 4

A: (10) Consider the given expression as shown below:

Q: QUESTION 4 The area bounded by the curves y = ²+1 and y =I+1 from intersection point to intersection…

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Q: QUESTION 6 Find the curvature of r(t)= (cos t, sin t, t?) at t =n/2.

A: Since not a particular question asked as per guidelines solution to only first question(i.e Q 6) is…

Q: Question 9. A circular helix in ryz-space has the following parametric equations, where 0 ER. r(0) =…

A: Here,  xθ=4cosθyθ=4sinθzθ=3θ

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 E R. 4 cos…

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Q: Question (1): The arc of the parabola y = x2 from (1,1) to (2,4) is rotated about y-axis. Find the…

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Q: Problem 11 (i) Find the area bounded by the polar curves r = 0 + 1, r = 0+3, 0=0, and 0 = 2 (ii)…

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Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

A: Given that  Z=x^2+2y^2  Point (-1,-1,3) To find teh point lies in p

Q: What is the arc length of the polar curve r = 1 – sin 0 for 0 < 0 < ? 2 (a) 2(v2 – 1) (b) 2 - V2 (c)…

A: Given polar curve is: r=1-sinθ   , 0≤θ≤π2

Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: A curve in spherical coordinates x for the line element ds? = (dx')² + (x') (dx?)? + (x'sinx?)…

A: Arc length is

Q: Consider the following parametric equation. x = 7(cos 0 + 0 sin 0) y = 7(sin 0 – 0 cos 0) 11 What is…

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Q: ind the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π (b) r = 4 sin…

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Q: A circular helix in ryz-space has the following parametric equations, where 0 E R. x(0) y(0) z(0) 4…

A: L(θ) = arc length of the helix from the point P(θ) to the point (4,0,0) P(θ)=(4cosθ ,4sinθ, 3θ)…

Q: Question 3 Find the value of J sinydx+ (xcosy-sinyldy, where Cis any curve from (2,0) to (1, T). Ca…

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Q: following equation aU (1,1). TC with U (0,t)= 0, = 0, and U (x,0)= sin 2. %3D %3D %3D at

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Q: Question 1 Let D be the region of the plane bounded by the curve C parameterized by 7(t) = [3 cos(t)…

A: It is given that, r→(t)=[3cos(t)-cos(3t)]i^+[sin(3t)-3sin(t)]j^, 0≤t≤2π   It can be written as,…

Q: Question 4 Let w aXu(q) + bX.(@) € T,S such that |lw||= 1. Then the normal curvature to the surface…

A: Solution and explanation is below

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

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Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, (ii) r = 2(1+ sin 8), 0<0< 27, 0<0< 2n.…

A: We have to find arc length of give curve after that we have to find relationship between their…

Q: QUESTION 14 The equation of the tangent plane to z=f(xy) =x² siny at the point (1,0,0) is given by…

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Q: Question 2 Suppose an object is moving along the unit circle. (æ(t), y(t)) Find the correct relation…

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Q: Identify the surface whose equation is given. p = sin(8) sin(4) O a sphere of radius - centered at…

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Q: QUESTION 14 Which one of the following points lies on the curve r= sin 0-5. (5, 0) o (5, 2n) o (-5,…

A: In this we find that point which lies on the given curve.

Q: Calculate the arc length of the polar 6 sin e + 8 cos 0, 0<0<T. curve r =

A: Solution

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 E R. 4 cos…

A: The given parametric equations are, x(θ)=4cosθy(θ)=4sinθz(θ)=3θ Given, arclength of the helix is…

Q: KS is tangent to the circle at T. secant KR contains P, the center of the circle. PR and PT are…

A: Consider the given information. Let's draw the graph step by step given as KS is tangent to the…

Q: ind the points (x,y) at which the polar curve r=3+3sin(θ),−π/4≤θ≤π/4 has a vertical and horizontal…

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Q: Question 2 Let F(x, v. 2) = -2y7 + 2xj. Use Stokes' Theorem to find 17-d7, where C is a circle…

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Q: Question 9. A circular helix in ryz-space has the following parametric equations, where 0 e R. z(0)…

A: The arc length using parametric equation is:  Lθ=∫0θdxdθ2+dydθ2+dzdθ2dθ…

Q: Question Seven a) Show that: dx = sin" +c b) If x-a cost+ In an), y=a sint , show that = tan x. dx…

A: radius o curvature  is given by  R=y'2+132y''

Q: Express the circle specified by r = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

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Q: Consider the following parametric equation. x = 3(cos 0+ 0 sin Ø) y = 3(sin 0 -0 cos 0) What is the…

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Q: What is the arc length of the polar curve r = 1– sin 0 for 0 <0 <? (a) 2(v2– 1) (b) 2- v2 (c) 2v2…

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

Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: The parametric equations: x = a a cos 8,y = a sin 0;0 <e< 2n, define a curve called an asteroid

A: Given: The parametric equation is where 0≤θ≤2π   To determine: The slope of the tangent wrt θ i.e…

Q: Question 3, Let o(0, 6) = (cos e sin o, sin 0 sin ø, cos o) be a parametrization of the unit sphere.…

A: let σθ,ϕ=cosθ sinϕ, sinθ sinϕ , cosϕ be a parametrization of the unit sphere. claim- to show that…

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 e R. 4 cos…

A:

Q: Consider the following parametric equation. a = 20(cos 0+0 sin 0) y = 20(sin 0-0 cos 0) What is the…

A: Consider the given information. x=20cosθ+θsinθy=20sinθ−θcosθ The formula of length of the curve in…

Q: Question 2 Find the length of the curve r(t) = (3 cos t)i + (3 sin t)j + 2ek, Osts3.

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