Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line segment from (0,0,0) to (3, 1, 0). I

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Q: Problem 1. a) Find the QR Factorization of matrix A =2 b) Use the QR Factorization in part a) to…

A: Given: A=21-11 Let u1=2-1, u2=11 (a) To write A=QR, where Q is orthogonal matrix . We first use Gram…

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Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

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Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

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Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: 5-find for y= (r² + 1)1 ,x (4r + 1)2 (use chain nule) %3D dx A)y Vr+1 (r2+1) dx dy r(4r + 1) B) dx…

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Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: Integrate f(x,y) = x² + y² over the triangular region with vertices (0,0), (17,0), and (0,17). The…

A: Given: fx,y=x2+y2. We have to integrate the given function over the triangular region with vertices:…

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: | (xy dx + 2y dy)

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Q: Find for the curve dx In (2x) + 5xy + y = 3.

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Q: Let the curve C be the line segment from (0, 0) to (3, 1). Let F = ⟨2x-y, 4y-x⟩ Calculate the…

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Q: | 5y? dx +xy dy

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Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

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Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…

Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as