Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

Q: dr. Let f(z) =z. Find from z-0 to Z-4+2í alongthe curve C given Z=21 to z=2i

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Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: (a) Compute the arc (1,3, 1/3). F(t) = (t, 3, t) between the points (0,3, 0) and length of the curve

A: These 2 are unrelated problems as anyone can be solve without any help of another. So by Bartleby…

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at…

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Q: et C be a portion of a curve from (2,0) to (2,2). Let F(r, y) = (tan(2?) +2, ) Is F conservative?…

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

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

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Q: 1. Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

A: Given: Curve y2=x2(1-x)----(i)

Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

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Q: Let C be the curve defined by T(t) = (2 + 2 sin(t), 3 – 2 cos(t)) for 0 < t < 4x=²) dx + (2xyev" +…

A: Given the integral is ∫Cy2exy2+4x-2dx+2xyexy2+2dy. Rewrite the integral as ∫CF·→dr→:…

Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Q4. Let C be a portion of a curve from (2,0) to (2, 2). Let F(r, y) = (tan(2²) + e²", 2.re²y + cos…

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Q: Suppose that a particle following the given path c(t) flies off on a tangent at t = to. Compute the…

A: Consider the path of the particle           c(t) = (2t2, t3-4t, 0) The velocity of vector is…

Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Let C be the curve defined by r(t) [6 cos(t) – 5 cos (t), 6 sin(t) – 5 cos(t) sin(t), cos(t)] for 0…

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Q: Let F= 3xyi + 2x² j and suppose C is the oriente curve shown in Figure 28. Evaluate F.ds both…

A: The line integral ∫CF·ds involves the integration over a specific path. In general surface,…

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: 13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: To find the linearization Lx,y,z of the function fx,y,z=tan-1xyz at 1,0,0

Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

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Q: Integrate f(x,y) =x+y over the curve C: x² + y = 49 in the first quadrant from (7,0) to (0,7).

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Q: 3. Let f(x, y) = xy² + x°y². Find an equation for the tangent plane at (x, y) (-1,2). %3D

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Q: Let F(x, y) = -z|. Let C be the curve parametrized by (t, cos(t), sin(t)), where 0 <t<. y Evaluate:…

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Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

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Q: Let curve C be the arc of x2 + y2 = 16 traversed once counterclockwise from (0, 4) to (0, -4). Let…

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Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: 7. Let F = (2x sin(y)e", x² cos(y)e*, z² sin(y)e*). Find along the path c:T = (sin(t), t, cos(t))…

A: F=2xsinyez, x2cosyez, x2sinyez curlF=ijk∂∂x∂∂y∂∂z2xysinyezx2cosyezx2sinyez⇒curlF=0 So, F is a…

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: Let C be the closed curve starting at (0, 1) traveling along the parabola y = (x – 1)? up to the…

A: Using Green's Theorem we solve the above question.

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

A: According to the given information, it is required to use green’s theorem to evaluate the integral.

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...

Q: 3. Find S. F · dr where F(x,y, z) = (3y²e*, 6ye* F(t) = (sin t, ,2-) for 0 <tsn. 1+3) and C is the…

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