z = a? – a? C a +y+z = a² + a

Q: 1. Let S be the surface generated by the curve +y+4= 0 when it is revolved about the z-axis. (a)…

A: y = x2 - 4 (a) we choose x, θ as perameter = (x, - (x2 + 4) cos θ, -(x2 +4) sin θ)   (b) dr→dx= (1,…

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: - Use the graphs of = irection in which the curve is traced as t increases. = f(t) and y = g(t) to…

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Q: et C be the curve of the intersection of the two surfaces a² +} = z and 4x2 +y} +? =9. nd let L be…

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Q: Consider the curve C shown in the accompanying figure, which is the intersection between the…

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Q: 10) The line x = -1+t,y = 2 +t,z 2t + 7 intersects the surface z = x2 + y?. Find the cosine of the…

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Q: What is true about the rose curve r= sin (990)? t has 99 petals and minimal domain D=[0,7) (b) It…

A: Given, the rose curve                              r=sin99θ

Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

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Q: Q1. (a) Given two points P(6,3,1) and Q (5,0,0), find the parametric equations for a smooth curve,…

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Q: (а) Given two points P(6, 3,1) and Q(5,0,0), find the parametric equations for a smooth curve, C:x =…

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Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: 3. Below is a curve C, which is the intersection between the surfaces S: z = 4 -x? and S2: z + 2x…

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Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: 3. Below is a curve C, which is the intersection between the surfaces S1: z = 4 -x? and S2: z + 2x…

A: A is the correct answer.

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: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

Q: For the level curve f(x,y,z)=12 for f(x,y,z)= 4x2 − 2y2 + z2 at the point (2,2,2), find the…

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Q: Consider the curve r= (t,1–2t²,-1-2t?), t= – 1 Find the equation of the normal plane of the curve at…

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Q: 8) Consider the oriented curve C given by C=C₁U C2, where C₁: y = x³, and C₂: y = x², as shown in…

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Q: s) The given curve is rotated about the x-axis. Find the are √2x +3,0 ≤ x ≤ 6. of the resulting…

A: Introduction: The formula for the surface of revolution of the curve is given by,…

Q: 6. Let a curve be parameterized by x = t³ – 9t, y = t+ 3 for 1 < t< 2. Find the ry coordinates of…

A: Given that

Q: em #4: Let C be the curve of intersection of the surfaces ア= 4e* and for 0 <x < 4. Compute the…

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

A: If f is continuous and non negative on the interval α≤θ≤β with 0&lt;β−α≤2π. Then  Arc length of…

Q: Curves C and C2 are parametrized as follows: C, is (x(t), y(t)) = (t,0) for – 1<t<1 and C2 is (x(t),…

A: Given that curves C1 and C2 are parametrized as follows:   C1 is (x(t),y(t)) =(t,0) for -1&lt;= t…

Q: Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a…

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Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

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Q: Use Green's theorem to evaluate ſ. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: We have to evaluate the integral ∫5xy+x2+y2dx+x2-ydy over the closed curve C. Comparing with…

Q: 1. Let F(x, y) = (1 — y, ½x³ +e³²), and let C with the position vector r be the portion of the…

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Q: Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: c) By using Green's theorem evaluate OUIM GUTM U where C is a closed curve starting from the origin…

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Q: For a clockwise-oriented simple closed curve C' bounding a region D, what is the relation between…

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Q: Consider curve C which is the intersection of the surfaces shown in the attached figure. x = y² +3…

A: Given is the curve. The object is to approximate the given integral.

Q: The length of the curve that results from the intersection of r = 1,0 <0 < T,0 < ¢ < 0.5n, with 0 =…

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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: Consider the oriented curve C, which is the intersection, in the first octant, of the surfaces shown…

A: Given that  C is the intersection of the surface 1 and surface 2 Surface 1: x-22=y-1 Surface 2: x +…

Q: Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P…

A: Given:

Q: 10) Consider the oriented curve C, which is the intersection, in the first octant of the surfaces…

A: Given that Surface 1: y-22=x-2 Surface 2: y+z=4 Fx,y,z=-x, y+z, z2 Find the value of ∫CF·dr

Q: (a) Sketch the curve f0)=|1+3sin(20j. for Oss Write down on the groph the valuer of thie xand y…

A: Note: Hi! Thank you for the question. As per the honor code, we'll answer the first question since…

Q: Consider the curve y = (x + 1)√√x. a. Show that y' 3x+1 2√√x b. Bob claims that there is therefore a…

A: We are given the equation of the curve y=(x+1)x we need to show that y'=3x+12x and check whether…

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Given 급 (1+ 블" -를 -용), dy * = k). What is the value of k such that y is perpendicular to the curve…

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Q: Let a, b > 0. Show that S = {(x, y) E [a, 00) x R| - = 1} is a smooth curve.

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Q: Find the length of the curve C defined parametrically by C: x(1) = e' cos t, y(t) = e' sin t, 0 <t <…

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Q: Consider the following curves C1 : x³ + y³ = 1 C2 : z³ + y³ = 9 C3 : y= x+1 C4 : y = 0 that are…

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Q: Consider the following. x = t, y- In(t) (a) Eliminate the parameter to find a Cartesian equation…

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Q: Evaluate S,lz| dz for the curves C1 and C2, both of which begin at a = 1 and end at b = -1. The…

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Q: 10) Consider the oriented curve C, which is the intersection, in the first octant of the surfaces…

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Q: 2. Neatly and accurately, sketch level curves for z = -2, -1,0, 1,2 for the following surfaces.…

A: a) The given function is z=x2-4y2   ...(1)we have to find the level curve for the values…

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: 1st we will form a differential equation from given data and then solve it to get the curve