(1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0) (1.-13) hence evaluate Fdr. (0,0.0)

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: An object is moving along a path defined by the graph  x^2+y^2=18 Compute  dy/dy, if dx/dt=-2,…

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

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Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: Find the approximate solution of the Poisson equation uxx + Uvy = -1, x| < 1, ly| < 1 u = 0 at x =…

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Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: Find all the second partial derivatives. T = e-4r cos(0) -4r 16e cos (0) Trr %3D Tre 4e 4"sin (0)…

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Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: The student should estimate the equation 0.24 0.24 + tan [0.247 + 2(0.27)n] π 1 1 =-+-tan(Tx + 2ny)…

A: Given function: gx,y=xπ+xπtanπx+2πy Point: 14, 14 To estimate: 0.24π+0.24πtan0.24π+20.27π Formulas…

Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: Find the differential of y = = sec 4x + csc24r %3D O dz (8sec 4xtan4x- 8csc 4xcot4r)dy %3D O dy =…

A: Explanation of the answer is as follows

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: I need help with 1a)

A: straight line becomes y=x

Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

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: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

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Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: computes curve length for 0

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Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

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Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

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Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Find all the second partial derivatives v = sin(2s^2 − t^3 )

A: Consider the the function  v=sin2s2−t3

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

A: Here I am attaching image so that you understand each and every step.

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

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Q: Let W=x*yz.compute the differential dw.

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Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Q: Find the general solution of a) (2wv- tan w) dv + (v^2 - v sec^2 w) dw = 0

A: (a) The differential equation is given as (2wv-tan w)dv+(v2-v sec2w)dw = 0 Compare it with Mdv+Ndw=0…