6) a) Given z= f(x, y) =, evaluate f(x y) from (2,1) to the (1.95, 1.05) and calculate |Az|. b) Use the total differential to compute |dz| (Write each result exactly)

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Q: 22 Evaluate the line integral |F-ds where F= 2xyi +(x-y')j and C is (a) y=x from (0,0) to (1,1) (b)…

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Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: 22 Evaluate the line integral F-ds where F = 2xyi +(x-y')j and C is (a) y=x from (0,0) to (1,1) (b)…

A: You asked to solve Q2 that is question (b).

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Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: (1) (a) Show that the line integral tan(y) dr +x sec (y) dy is independent of path, where C is any…

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Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

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Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: 5. Calculate the double integral f, 2x cos(xy) dA , R = [0,2] × [0, 7]

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Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x -y . Use…

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Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: Given: xD(D+x)

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: ¡(z+1)dz 3 where C is z+2|= |z+2\=% z'-4z

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Q: Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine…

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Q: 1. Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

A: We have xdy+ydx=3xdx We know that d(xy) = xdy +ydx Therefore , d(xy) = 3xdxIntegrate above equation…

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: Given: f(x,y) = 2x²y³ and the points (1,2) and (1.1, 2.05) a.) Find f(1,2) and f(1.1,2.05). Then…

A: Here we want to find ∆Z using the function values and total differential.

Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

A:

Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

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Q: Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)

A: Given query is to find the the line integral for the y = 2x over y = x2.

Q: Differentiate implicitly to find z, and zy given x² - Vỹ + 22 = 2xyz.

A: topic - partial differentiation  answer is -17/56

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Show that the function f(x + iy) = Vlæ|ly| satisfies the Cauchy-Riemann equations at the origin but…

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Q: Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(1, y) = In(r +y?) at…

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Q: Solve by Laplace transform Utt – 9urz = 0, 0 0 %3D u(0, t) = u(r, t) = 0, %| %3D u (x, 0) = 0,…

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Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

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Q: Q2 Evaluate the line integral | F•ds where F = 2xyi +(x- y²)j and C is (a) y = x from (0,0) to %3D…

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Q: Let u(x,y,t)=(1/t)exp[-(x²+y²)/4t] where exp denotes e to a function. Show that u(x,y,t) satisfies…

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Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: v) ₁ √√¹-x² sin(x² + y²) dzdydx fő

A: Given is  ∫01∫01-x2∫01sinx2+y2dzdydx In order to solve this integral it is needed to first convert…

Q: Consider F(x, y, z)=e-2 yi-y³/²zx²j+ln(22)k and calculate the divergence of F.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 9. Find the bounds of integration a, b, c, d such that T (a, u) dydar. f(x, y) dædy =

A: x≤y≤4x=y →y=xy=40≤x≤4x=0 to x=4

Q: (1) Show that F(x, y) : (2x + y, x - y) is path independent and use the fundamental = theorem of…

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Q: 5. (a) ( If ryz² + x²yz + ry²z = e*v², compute . (b) Let f(r,y) be some function. Set up the…

A: (a) The equation given in the question is: We need to evaluate  This represents the derivative of…

Q: 2 Find the orthogonal trajectories of r=asin? 0 where a be the arbitrary constant.

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Q: 7. Verify Green's Theorem for O (6+ x²) dx + (1 – 2xy) dy where C' is shown below by (a) computing…

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Q: Find the total differential for the function w = 13z ysin x. dw = 13z ysin xdx-13z sin xdy-26z ysin…

A: Consider the function: Let,  w=13z3ysinx=fx,y,z The total differential of the function is given by…

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

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Q: a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider…

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Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: Let F(r, y, z) = (y² + 2z, 2ry + 4, 2a), and let the curve C be described by x = t, y = t, z = t3…

A: