Problem 4. Find fe F- di where C is a circle of radius 2 in the plane z + y+ z = 9, centered at (4, 4, 1) and oriented clockwise when viewed from the origin, it F = -3zj+ 2yk LF. dř =

Q: Problem 9. Consider the surface 4x² + 16y? + 4z² = 24 and the point P = (1,1,1) on this surface. A.…

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Q: Question 16 Find the area of the region bounded by the curve y2-4x and the lines x = 1 and x = 4.…

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Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u - v, u…

A: According to guidelines we should have been able to solve only first question at a time #3

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: Question 15 Find the area bounded by the curve y = -x 16 A 8 square units B 16 square units C10…

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Q: Problem 3. Find the shortest distance between the point P (0, 1,0) and the line l given by x = 1-t,…

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Q: Question 4. Match the equation with the surface it defines. Also, identily each surface by type.…

A: Given: Equations 1. x=y2-z2; 2. x=z2-y2 and the graphs

Q: Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 9:)i + (7x + y) j + (6y – =) k and…

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Q: Problem 1. Parametrize the following surfaces: (a) 2x + 3y + z = 6. (b) z = 9 – Vx² + y?. - (c) x² +…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…

Q: 6. State the center and radius of the circle: x + y² – 4x + 2y = 16 Center: (-2, 1) and r = 21…

A: The solution as follows :-

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   y = 1 -x2…

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Q: Question #8 I need the curves as well

A: Question #8 The provided sample means are shown below: Xˉ1=12.3\bar X_1 = 12.3 (For those taking the…

Q: Problem 1. Find Fn dS if S is the sphere (x-1)´+y+z=1 , S and F(x, y,z)= (x³, x²y , zy°) . 2

A: n = 820 , x=22 Po=xn=22820=0.0268 npo(1-Po)=820(0.0268)(1-0.0268)     = 22(0.9732)           = 21.41…

Q: Problem 3: Evaluate ff,F· dA using Gauss, where F = half of the sphere x2 + y? + z²2 = 9. (2²x, y³ +…

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Q: #10

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Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: Problem 1 Evaluate the line integral / 2* ds, where C is the line segment from (3,0) to (0,4) in the…

A: Given line integral ∫Cx2ds, line segment (3,0) to (0,4)

Q: Problem 8 Consider the surface z = f(x, y) whose level curves are below (some of which are labeled)…

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Q: Problem #3: Consider the function E(x, y, =) = 2r2 + y? – 2: - 2 and the level surface E(x, y, =) =…

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Q: Problem #6: Given the function z = sin(x) * cos(y) ) + sin?(x) * cos²(y) For the range 0<x<47T and…

A: As per the question we have the following bivariate function : z = sin(x)cos(y) + sin2(x)cos2(y) ,…

Q: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

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Q: 1- What is the value of f 3z2+7z+1 dz z+1 (a) If C is the circle |z+1|=1. (b)If C is the circle…

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Q: QUESTION 2: Find equations of the Normal plane and Osculating plane of the y = 2t , x = 2 sin 3t , z…

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Q: Problem 1 (a) Let f (z) = x² + iy² where x and y are the real and imaginary parts, respectively of z…

A: As per our guidelines, we supposed to solve the very first question if multiple questions are posted…

Q: Find equations of (a) the tangent plane and (b) the normal line to the surface 2(x−2)2 + (y−1)2 +…

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Q: Find the centroid of the region above the curve (shaded in green) in Figure 4. This region is ranges…

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Q: Problem 4 The helix r(t) = (cos(rt/2), sin(rt/2), t) intersects the sphere x2 + y2 + z2 = 2 in two…

A: We will find tangent vector of helix at point of intersection and the find angle of this tangent…

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: Problem 2 (a) # fc [37 – + ] dz (z+3i)* Evaluate -- - z+3i where C is the circle Z + 3i| = 7+ 7, 0 <…

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Q: Question 7 2 pts Find the curvature k of the x2 curve C : :1 at 9 | 16 + the point (4, 0) 9. 3 3 16…

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Q: Problem 12 Find an equation for the plane that is tangent to the given surface at the given point…

A: In this question we have to find the equation for the plane that is tangent.

Q: Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y =…

A: Given the region bounded by the circle x2+y2=9. The height of the cross-section is 3-x and its…

Q: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Problem 4 A mound of blue powder dye is placed on a flat surface in the x-y-plane as shown. The flat…

A: Given: The top surface of the mound is defined by zx,y=sinxsiny and the surface is a square of the…

Q: Problem 2: Let C be the boundary of the triangle with vertices 0, 2+ i, and 3i. (a) Find the line…

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Q: Question 3 Find the point(s) of intersection of the curves r = 6 and r = 12 sin e OA 6 * (6.5)(6) 3…

A: To find the intersection of the curve r=6 and r=12sinθ

Q: Situation 7. Find the tangent to the parabola y? = 6x – 3 perpendicular to the line x + 3y = 7. 26.…

A: Given that parabola y2=6x-3 , tangent perpendicular to the line x+3y=7To find : equation of tangent…

Q: Problem 4: Find the vector function that represents the curve of intersection for the following…

A: Given surface 1 is, x2+z2=9 Given surface 2 is, x2+y2+4z2=25........(1)

Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: Problem 1. Parametrize the following surfaces: (a) 2r +3y +2 = 6. (b) 2 = 9 - V + y?. (c) r + = 4.…

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Q: Problem 3. Find the curvature of the curve given (t). at the point ( LD

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Q: Problem Set in Areas Between Two Curve 1.0 4 0.8 0.6 + 3. Derive a formula for the area of a sector…

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Q: fc x2 dx+x2 dy C consists of the arc of the circle x2 +y2 = 4 from (2,0) to (0,2) followed by the…

A: Given integral is ∫Cx2dx+y2dy from the point (2, 0) to (0, 2) by the line segment from (0, 2) to (4,…

Q: Problem 1. Evaluate x-y+z-2 ds where C is the straight-line segment x = t, y = 1-t, z = 1 between…

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Q: Problem 1. ad the points on the sphere r² + y² + z? = 9 that are closest to and farthest away

A: Given,           x2+y2+z2=9                        (1)

Q: Problem II We consider a parametrization of a regular surface S, given by X (u, v) = (u+2v, 2uv, 2u…

A: Here the equation of the tangent plane to the surface will be Xu×Xv.x-6,y-8,z-2=0 where X=Xu,v is…

Q: Question 13 Find the center of curvature of the curve y=Inx at (1, 0). A (4, 3) B) (3, 4) (3, -2)…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.