Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x − 2y = 4. A possible way for the parameterization of the curve C corresponds to:

Q: Find the equation of the tangent plane Pr to the surface S: x2 + y? +z² = 9 at (2, –1, 2)

A: The equation of the tangent plane to the surface f(x, y, z)=0 at a, b, c is defined as: fxa, b,…

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

Q: 1. Use the Stoke's Theorem to evaluate y'dx + xy dy + xz dz, C where C is the bounding curve of the…

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Q: Find a parameterization for the curve y = 7 – 2x that passes through the point (0,7, 3) when t = 2…

A: To find the parameterization of the curve

Q: At what points does the curve r(t)=(t,t,14t) intersect the surface z=x2+3y2?

A: Given: rt=t,t,14t, z=x2+3y2 for finding intersection point of curve and surface we put point t,t,14t…

Q: At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter…

A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

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

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Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

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Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

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: Find the area of the surface generated when the given curve is revolved about the y-axis. y-(3x)13,…

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Q: dy In the xy-plane, the point (0, 2) is on the curve C. If 4t for the curve, which of the following…

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Q: Find the points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

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Q: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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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: for y^2 - z^2 =1, find the point(s) on surface nearest to origin

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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: Consider the curve C which is the intersection of the surfaces shown in the accompanying figure. z=4…

A: The graph of a curve C is given. The objective is to integrate the function -z+2y+3x along the curve…

Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 & C2 then substitute the x,y,z values into the line…

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: et f(z, y) = for (z, y) # (0,0). Find the level curves of 2 + y²

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Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

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Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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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: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: 5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

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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: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

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: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

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: If z³ + y® – z°y12 = 1, find in terms of z and y. dy Using your answer for , fill the following…

A: x3+y6-x10y12=1differentiating w.r.t…

Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the…

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Q: A curve in the æy-plane is defined by (x(t), y(t)), where x (t) = t² and y (t) = tª + 1 for t > 0.…

A: Option A is correct answer, Detailed explanation is given below.

Q: Let C be any curve.

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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: z = a? – a? C a +y+z = a² + a

A: S1=a2-x2 S2: x+4+z=a2+a Let us start solving above equations

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: 3) Consider the curve C which is the intersection of the surfaces shown in the attached figure. If…

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

A: knlk

Q: Given w = f(x, y, z) = 4r + y + 4z². Sketch the level surface of the function for w = 1.

A: For the function of the form: w=fx, y, z, the level surfaces are defined using the equation, f(x, y,…

Q: Show that the Bézier curve with control points Po = (1, 4), P = (3, 12), P, = (6, 15), P3 = (7, 4)…

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: Let C be the curve of intersection of the cylinder x2+y? = 2 and the hyperbolic paraboloid x? – y? +…

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