2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin 3.x + cos 3 x, x = 3t, y = t,0 < t < 1.

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Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: 1. Find the work done by F(x, y, z) = (-y,–x, z) on a particle that moves along the curve R(t) (2…

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and

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Q: 3.) Calculate the curve integral f (1 – a² + y²) dx + (1 + x² – y°) dy. Here C consists of the…

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Q: 3. Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

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Q: - Use the information to find and compare Ay and dy. Function x-Value Differential of x y = x+ x = 2…

A: y=x4dy=4x3dxGiven that dx=0.2, x=2dy=4(2)3(0.2)dy=6.4

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: 14.w.3 Find Ihe arcan region for he fllowwiy Regian honded.by.y= X- y=D and S= 2

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Q: (0. ) : If f(x, y) = 12e cos x + 3 cot y, then the total differential of f at is : J, df = -12 dx 6…

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Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: dy Nrite the linear DE (2y sinx – cos³x) dx + cos x dy=0 in standard form - +yP (x) =Q (x). dx (A)…

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Q: 17. Evaluate the line integral xe" dx +y sin yªdy along the triangular path consisting of the line…

A: Consider the given integral. I=∫Cxex2dx+ysiny2dy The given points are 0,0,2,3,1,0,0,0. Now, draw all…

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Q: 4- Calculate the Laplacian of the following functions: (a) T e* sin4y cos 3z. (b) V = x° x^+3xz y-…

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Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: 1. 5. Find the value of the line integral. (x - y) dx- 2.xy dy C:r(t)=2 cos ti + sin ti

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Q: Find the differential dy: y = In (sec2 (3* )). -2a+5 O tan (3-2+* ) dæ -2r+5 dy = (x – 1)…

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Q: -2y The line integral (e sin x) dx+(x' +3y)dy with path F (t)= (8cost, 8 sint) such that 0sts2n. Set…

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Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: 3.) Calculate the curve integral (1 – x² + y²) dx + (1 + 2² – y²) dy. Here C consists of the curves…

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Q: Find the differential and evaluate for the given x and d/x of the function, y = 3x2- x+ 6, x = 2, dx…

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Q: 1.6 Evaluate the line integral f x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

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Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: Q#03:Use Green's theorem to evaluate the line integral x³y² dx+ (cos5x – 2e2*y³)dy, where C is the…

A: According to the given information, it is required to evaluate the line integral using Green’s…

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: (dy = arctan dx, (i) Use the facts: dy and (dy/dt) to find dt d dx (dx/dt) ds (ii) Use the fact that…

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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: computes curve length for 0

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Q: 1. [[1 + y*J sin(xy) + xycos(xy)]dx + {[1 + x] cos(xy)- xysin(xy)} dy=C

A: Suppose we have equation,                M(x, y) dx + N(x, y) dy =0 Firstly we check that is it…

Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: (2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

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Q: b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x,…

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Q: 1. Sketch the direction field and solution curve for the given DE and condition. Sketch the…

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: It is given that,xey+sinxy+y-ln2=0.We have to find the value of dydx at the point 0,ln2.

Q: Consider the functional S[y] = − y(2)² + √² ² + [² dx (31/1²) 2 with right-hand boundary condition…

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Q: 28. Suppose you follow the spiral path C: x = cos t, y= sin t, and z= t, for t20, through the domain…

A: NOTE: You have posted a question with multiple subpart, we have given answers to the first three…

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

Q: Question 4 Evaluate the line integral: (i) of T(x) = 4x^3 along the line segment from (-2,1) to…

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Q: 6x Find the linearization L(x,y) of the function f(x,y) = e cos (y) at the points (0,0) and

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Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

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