3 Integrate f(x,y,z) = x + √√y - z³ over the path from (0,0,0) to (3,9,3) given by C₁: r(t) = ti + t²j, 0≤t≤3 C₂: r(t) = 3i+ 9j + tk, 0≤t≤ 3.

Q: Integrate G(x,y,z) = x over the parabolic cylinder y=x², 0≤x≤√√2, 0szs2.

A: The objective is to integrate Gx,y,z=x  over the parabolic cylinder y=x2, 0≤x≤2 and 0≤z≤2. The…

Q: (x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x =…

A: We will find the required.

Q: Let f (x, y) = zy(z²–y") (z²+y²) if (x, y) + (0,0) and f (0,0) = 0. af af (a) If (x, y) # (0, 0),…

A:

Q: Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az…

A: We have to find   dz and delta z and compare the the values.

Q: Suppose f(x, y) = xy² + 4. Compute the following values: f(4,-5)= ƒ(−5, 4)= f(0,0)= ƒ(5,-5)= f(t,…

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: f(x, y) = √√2x² + 5y² fz(0, 1) =

A:

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Suppose f(x, y) = xy² + 3. Determine each of the following: f(0, -2)= f(-2,0)= f(0,0)= f(-3,-2)=…

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Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: 3 For f(x,y) = In x+y°, 4,8)

A:

Q: Let A(t) = 3ti+2]-4k, y B-21-21-3tk and C(t)=-1+3tj+6k. find Ax (B-C) dt

A: