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: Q2) f(x,y) = 2xy x(s,t) = 3s-2t and y(s, t) = s²+4t. Find Je Je as at

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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),…

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Q: f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

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Q: b) Let X = Cle,e+ 2] and define T:C[e,e+2] → R by re+2 T(z) = | 1(t)dt, r€ Cle,e+2] Show that T is…

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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: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

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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: + x(x*+ zy² + ig) dy= luy) dy 2. 2. 2) 3(x y) dx -

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let y=f(t) be as shown. Y ↑ (1,4) Show all work a) Express flE) in terms of the "switch". b) Find c)…

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Q: f(x, y) = √√2x² + 5y² fz(0, 1) =

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Q: If FGx) = -2x+s firid f(z)

A: Given: if f(x)=-2x+54To find: f(1)

Q: Зху? — 3x nint of r

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Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

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Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: Consider f(x, y) = (2x² + xy + 1, xy, x² + y²) and let c = (1,-1). Find Df(c) by definition.

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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: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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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: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

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)

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

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Q: 2. Let f(x, y) = 4x³y² + 3x²y³, find: (a) Vj (1,2) (b) f(1,2), where u = 17-17

A: (2)  Given that  f x, y = 4x3y2 + 3x2y3  (a)     ∂f∂x = 4y2∂∂xx3 + 3y3∂∂xx2       ⇒ ∂f∂x = 4y23x2 +…